fermionic field quasi-bound states around black holes

Understanding the physical significance and spectral stability of black hole quasinormal modes is fundamental to high-precision spectroscopy with future gravitational wave detectors. Inspired by Mashhoon's idea of relating quasinormal modes of black holes with their equivalent bound states in an inverted potential, we investigate, for the first time, energy levels and eigenfunctions of the Schwarzschild black hole quantitatively. While quasinormal modes describe the characteristic damped oscillations of a black hole, the bound states of the inverted potential are qualitatively more similar to those of the hydrogen atom. Although the physical interpretation of these states may initially be of more academic interest, it furthers our understanding of open problems related to quasinormal modes in a similar spirit to Maggiore's interpretation of the Schwarzschild quasinormal mode spectrum. One surprising insight from the explicit calculation of bound states is that eigenfunctions corresponding to quasinormal mode overtones become rapidly delocalized and extremely loosely bound. This observation raises immediate questions about the common interpretation of quasinormal modes as excitations of the light ring region. Closely related, as a second application, we also explore the spectral stability of bound states and demonstrate that they can provide complementary insights into the quasinormal mode spectrum.

We study the N-partite coherences of GHZ and W states for free bosonic and fermionic fields when any n observers hover near the event horizon of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. We derive the more general analytical expressions for N-partite coherence, encompassing both physically accessible and inaccessible coherences in the context of the dilaton black hole. It has been found that the coherence of the bosonic field is greater than that of the fermionic field, while the entanglement of the fermionic field is greater than that of the bosonic field in dilaton spacetime. Additionally, the coherence of the W state is greater than that of the GHZ state, whereas the entanglement of the GHZ state is greater than that of the W state in curved spacetime. These results suggest that we should utilize suitable quantum resources and different types of particles for relativistic quantum information tasks.

It is generally believed that quantum entanglement in the maximally entangled states is greater than quantum entanglement in the non-maximally entangled states under a relativistic setting. In this paper, we study quantum entanglement for four different types of Bell-like states of the fermionic modes near the event horizon of a Schwarzschild black hole. It is interesting to find that quantum entanglement in the maximally entangled states is less than quantum entanglement in the non-maximally entangled states in Schwarzschild spacetime. From the perspective of quantum resources, the non-maximally entangled states may have more advantages in curved spacetime compared to the maximally entangled states. This is obviously different from the conclusions in previous paper. For two types of Bell-like states, quantum entanglement suffers sudden death under the Hawking effect of the black hole, and for the other two types of Bell-like states, quantum entanglement can exist forever regardless of the Hawking temperature. Therefore, we should choose appropriate types of Bell-like states to handle relativistic quantum information tasks.

No abstract available

Black holes, as characterized by the Hawking effect and Bekenstein-Hawking entropy, can be treated as a compact object carrying nontrivial quantum information obscured behind the event horizon. Thus, the black hole may convey and retract its quantum information to the nearby quantum probes via the surrounding mediator fields. In this paper, we investigate the effects of a quantum black hole on the reduced states of a pair of static qubit-type Unruh-DeWitt (UDW) detectors acting as a probe, using three complementary quantum information measures: concurrence characterizing entanglement harvesting, quantum discord, and Bell's nonlocality bound. This sheds light on the nature of the quantum state of the black holes. By treating the black hole as a tidally deformable thermal body under the quantum fluctuation of the mediator fields as observed in \cite{Goldberger:2019sya, goldberger2020virtual, biggs2024comparing}, we employ a post-Newtonian effective field theory (PN-EFT) to derive the reduced states of the UDW probes analytically. Based on this, we can easily obtain all three quantum information measures without encountering the complicated Matsubara sum of infinite thermal poles, as in the conventional approach based on quantum fields in curved spacetime. By tuning the relative strengths in the action of PN-EFT, we can extract the effects of the black hole on the entanglement, quantum correlation, and nonlocality bound of the UDW probe systems. Our PN-EFT approach can be extended to include the backreaction on the black holes in future studies by taking the higher-order PN corrections into account.

This paper investigates quantum obesity, quantum discord, and the quantum steering ellipsoid (QSE) for bipartite Gisin states that are subjected to Garfinkle–Horowitz–Strominger (GHS) dilation of spacetime on the second qubit. These three quantifiers are introduced to characterize quantum correlations beyond entanglement and can also function as entanglement witnesses. A monotonic decrease in the physical accessibility of both quantum discord as demonstrate in the results and quantum obesity as the dilation parameter increases within the region‐I of the second qubit. Conversely, in the anti‐particle region, the accessibility of quantum discord and quantum obesity stabilizes at finite values of the dilation parameter owing to the influence of the Pauli exclusion principle and Fermi‐Dirac statistics, subsequently increasing gradually. Notably, the QSE in the region‐I expand as the Dirac field frequency rises and the dilation parameter diminishes, while the opposite trend is observed in the anti‐particle region.

The chronology protection conjecture (CPC) was first introduced by Hawking after his semi-classical investigation of the behaviour of a spacetime with closed timelike curves (CTCs) in response to scalar perturbations. It is argued that there would be instabilities leading to amplification of the perturbation and finally causing collapse of the region with CTCs. In this work, we investigate the CPC by exactly solving the Klein–Gordon equation in the region inside the inner horizon of the non-extremal Dyonic Kerr–Sen (DKS) black hole, where closed timelike curves exist. Successfully find the exact radial solution, we apply the polynomial condition that turns into the rule of energy quantization. Among the quasi-resonance modes, only certain modes satisfy the boundary conditions of quasinormal modes (QNMs). QNMs in the region inside the inner horizon of the rotating black hole with nonzero energy have only positive imaginary parts which describe states that grow in time. The exponentially growing modes will backreact and deform the spacetime region where CTC exists, hence the CPC is proven to be valid in the non-extremal Dyonic Kerr–Sen black hole spacetime. Since the Dyonic Kerr–Sen black hole is the most general axisymmetric black hole solution of the string inspired Einstein–Maxwell-dilaton-axion (EMDA) theory, the semiclassical proof in this work is also valid for all simpler rotating black holes of the EMDA theory. The structure of the Dyonic KS spacetime distinctive from the Kerr–Newman counterpart is also explored.

In this comment, we point out a series of errors made by Senjaya in your paper (2024) \cite{Senjaya}. In particular, these errors involved the Dirac equation in the 3+1 dimensional Schwarzschild spacetime, tetrad field, curved gamma matrices, and the time-independent Dirac equation written in terms of the inner/scalar product between the gamma matrices and the orbital angular momentum (i.e., $\vec{\gamma}\cdot\vec{L}$). Besides, the strange/peculiar thing about all this is that even Senjaya \cite{Senjaya} citing Collas and Klein \cite{Collas}, where the (mathematical) formalism is correct, everything indicates that he ``ignored'' or ``forgot'' to use such formalism in your paper. Therefore, using Ref. \cite{Collas}, we show here the correct form of the errors made by Senjaya \cite{Senjaya}.

We examine the interaction between quantum test particles and the gravitational field generated by a black hole solution that was recently obtained in the consistent 4-dimensional Einstein–Gauss–Bonnet gravity. While quasinormal modes of scalar, electromagnetic, and Dirac fields have been recently studied in this theory, there is no such study for the quasibound states. Here, we calculate the spectrum of quasibound states for the test fields in a spherically symmetric and asymptotically flat black hole solution in the consistent 4-dimensional Einstein–Gauss–Bonnet gravity. The quasispectrum of resonant frequencies is obtained by using the polynomial condition associated to the general Heun functions. We also discuss the stability of the systems for some values of the Gauss-Bonnet coupling constant.

Dirac cloud is in absence in general relativity since the superradiance mechanism fails to work for Dirac fields. For the first time, we find a novel mechanism to support Dirac clouds, which is independent on superradiance mechanism. We study quasibound states of Dirac particles around a charged spherical black hole in dilatonic gravity. We find that the quasibound states become real bound states when the central black hole becomes extremal. We make an intensive study of the energy spectrum of the stationary clouds for different fine structure constant μM and reveal the existence condition of these clouds. Our result strongly implies that extreme dilatonic black holes behave as elementary particles.

In this work, we aim at solving the Teukolsky equations for a fermion with mass m e ≠ 0 in the presence of a rotating black hole with mass M. We consider two different regimes: m˜e=M−1me≪1 and a ω ≪ 1; m˜e≪1 and a ω ≳ 1. We treat each of these two regimes in different ways: we use a perturbative approach for the first, similar to the usual one employed for spin 0, 1, 2 and mass-less 1/2 fields, but with two small parameters (aω and m˜e ); as we shall see, the second can be treated with a semi-analytical approach. In a forthcoming paper we shall study the remaining two cases in which m˜e≳1 , while a ω ≪ 1 or a ω ≳ 1. The regime with m˜e≪1 , but a ω ≳ 1 is probably the most interesting from the astrophysics point of view, but this last two cases might be of some interest for the study of the interaction of fermions with very small black holes, which may be formed, for example, in the last stages of the Hawking evaporation.

In this paper, we study the greybody factors (GFs) for fermions with different spins and bosons in the regular black hole (BH) predicted by a non-minimal Einstein–Yang–Mills (EYM) theory. We investigate the effect of magnetic charge on effective potentials and GFs. For this purpose, we consider the Dirac and Rarita–Schwinger, as well as Klein–Gordon equations. First, we study the Dirac equation in curved spacetime for massive and massless spin-1/2 fermions. We then separate the Dirac equation into sets of radial and angular equations. Using the analytical solution of the angular equation, the Schrödinger-like wave equations with potentials are derived by decoupling the radial wave equations via the tortoise coordinate. We also consider the Rarita–Schwinger equation for massless spin-3/2 fermions and derive the one-dimensional Schrödinger wave equation with gauge-invariant effective potential. For bosons, we study the Klein–Gordon equation in the regular non-minimal EYM BH. Afterward, semi-analytic methods were used to calculate the fermionic and bosonic GFs. Finally, we discuss the graphical behavior of the obtained effective potentials and bounds on the GFs. According to graphs, the GF is highly influenced by the potential’s shape, which is determined by the parameterization of the model. This is in line with quantum theory.

In this article, we consider charged fermion particle radiation around Kerr – Newman – Vaidya black holes. Using the Hamilton – Jacobi method we derived the emission probability and the temperature of the Hawking radiations. We obtained that the temperature is equal to that due to scalar particles times a factor that contains some characteristics of fermions.

A hairy black hole (HBH) emerges due to matter surrounding the Schwarzschild metric when using the Extended Gravitational Decoupling (GD) approach. The fermionic greybody factors (GFs) and quasinormal modes (QNMs) as well as Hawking spectra and sparsity of HBH solutions are investigated. We consider massive and massless spin-1/2 fermions, along with massless spin-3/2 fermions. The equations of the effective potential for fermions with different spins are derived in HBH spacetime. Then, the rigorous bound method is used to calculate the fermionic spin-1/2 and spin-3/2 GFs. With the time domain integration method at our disposal, we illustrate the impact of additional parameters on the ringdown waveform of the massless fermionic spin-1/2 and spin-3/2 fields and, in turn, on their quasinormal modes. We then delve into investigating the Hawking spectra and sparsity of the radiation emitted by an HBH. Hairy parameters significantly affect the sparsity of Hawking radiation as well. We observe that the total power emitted by the BH increases both with α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and Q but decreases with l0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{0}$$\end{document}. Our study conclusively shows the significant impact of the additional parameters on important astrophysical phenomena such as quasinormal modes, Hawking spectra, and sparsity.

Expectation values of one-loop renormalized thermal equilibrium stress-energy tensors of free conformal scalars, spin-1/2 fermions, and U(1) gauge fields on a Schwarzschild black hole background are used as sources in the semiclassical Einstein equation. The back reaction and new equilibrium metric have been found at [ital O]([h bar]) for each spin field in previous work. In this paper, the nature of the modified black hole spacetime is explored through calculations of the effective potential for null and timelike orbits. Significant novel features affecting the motions of both massive and massless test particles show up at lowest order in [epsilon]=([ital M][sub Pl]/[ital M])[sup 2][lt]1, where [ital M] is the black hole mass, and [ital M][sub Pl] is the Planck mass. Specifically, we find an increase in the black hole capture cross sections, and the existence of a region near the black hole with a repulsive contribution, generated by the U(1) back reaction, to the gravitational force. There is no such effect for other spins. Extrapolating our results suggests a tendency towards the formation of stable circular orbits, but the result cannot be established in [ital O]([h bar]): the change in the metric becomes large and it changes its signature. We alsomore » consider the back reaction arising from multiple fields, which ultimately should be useful for treating a black hole in equilibrium with field ensembles belonging to gauge theories. In certain circumstances, however, reliable results will require calculations beyond [ital O]([h bar]).« less

No abstract available

We obtain fermion fluctuation equations around extremal charged black hole geometries in maximal gauged supergravity in four and five dimensions, and we demonstrate that their solutions display Fermi surface singularities for the dual conformal field theories at finite chemical potential. The four-dimensional case is a massless charged fermion, while in five dimensions we find a massive charged fermion with a Pauli coupling. In both cases, the corresponding scaling exponent is less than one half, leading to non-Fermi liquid behavior with no stable quasiparticles, although some excitations have widths more than 10 times smaller than their excitation energy. In the five-dimensional case, both the Fermi momentum and the scaling exponent appear to have simple values, and a Luttinger calculation suggests that the gauginos may carry most of the charge of the black hole.

No abstract available

We study the quasinormal mode spectrum and grey-body factors of black holes in an effectively quantum-corrected spacetime, focusing on the influence of near-horizon modifications on observable quantities. Employing scalar, electromagnetic, and Dirac test fields, we analyze the perturbation equations and extract the fundamental quasinormal frequencies using both the 6th-order WKB method with Padé resummation and time-domain integration. Our results show that quantum corrections near the horizon significantly affect the real and imaginary parts of the quasinormal modes, particularly for low multipole numbers and in the near-extremal regime. We also verify the robustness of the correspondence between quasinormal modes and grey-body factors by comparing WKB results with those reconstructed from the dominant quasinormal modes. Across all field types and parameter ranges considered, the WKB method proves accurate within a few percent, confirming its reliability in probing the impact of near-horizon physics. These findings support the use of quasinormal ringing and Hawking radiation spectra as sensitive tools for testing quantum modifications of black hole spacetimes.

We compute the quasinormal modes of massive scalar and Dirac fields within the framework of asymptotically de Sitter black holes in Euler–Heisenberg non-linear electrodynamics. We pay particular attention to the regime μM/mP2≫1,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu M/m_{P}^2 \gg 1,$$\end{document} where μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} and M denote the masses of the field and the black hole, respectively, and mP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_{P}$$\end{document} represents the Planck mass, covering a range from primordial to large astrophysical black holes. Through time-domain integration, we demonstrate that, contrary to the asymptotically flat case, the quasinormal modes also dictate the asymptotic decay of fields. Employing the 6th order WKB formula, we derive a precise analytic approximation for quasinormal modes in the regime μM/mP2≫1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu M/m_{P}^2 \gg 1$$\end{document} without resorting to expansion in terms of the inverse multipole number. This analytic expression takes on a concise form in the limit of linear electrodynamics, represented by the Reissner–Nordström black holes. Our numerical analysis indicates the stability of the fields under consideration against linear perturbations.

In this study, we have investigated the mathematical components of the Dirac equation in curved spacetime and how they can be applied to the analysis of neutrino oscillations. More specifically, we have developed a method for calculating the phase shift in flavor neutrino oscillations by utilizing a Taylor series expansion of the action that takes into account orders. In addition, we have used this method to assess how the phase difference in neutrino mass eigenstates changes according to the gravitational field described by the Johannsen spacetime.

In this paper we construct a scattering theory for the massive and charged Dirac fields in the interiors of sub-extremal Kerr-Newman(-anti)-de Sitter black holes. More precisely, we show existence, uniqueness and asymptotic completeness of scattering data for such Dirac fields from the event horizon of the black hole to the Cauchy horizon. Our approach relies on constructing the wave operators where the Hamiltonian of the full dynamics is time-dependent. To prove asymptotic completeness, we use two methods. The first involves a comparison operator, while for the second we introduce and employ a symmetry operator of the Dirac equation.

We study quasinormal modes of test scalar, electromagnetic, and Dirac fields in the background of a new analytic regular black-hole solution obtained as an exact solution of the Einstein equations sourced by a Dehnen-type matter distribution in [R. A. Konoplya, A. Zhidenko, arXiv:2511.03066]. The metric is asymptotically flat and characterized by a simple lapse function $f(r)=1-2 M r^{2}/(r+a)^{3}$, where $M$ is the ADM mass and $a$ represents the characteristic scale of the surrounding dark-matter halo that regularizes the central region. The effective potentials for all perturbing fields possess the standard single-barrier form, ensuring linear stability and the applicability of the WKB formalism. The quasinormal frequencies are computed using the sixth- and ninth-order WKB methods with Pad\'e corrections and verified by time-domain integration, both approaches showing excellent agreement. The parameter $a$ leads to a moderate increase in the real oscillation frequency, while the damping rate remains almost unchanged, producing only small corrections to the Schwarzschild spectrum. Since such deviations become appreciable only for unrealistically dense halos, our results confirm that the quasinormal spectrum of astrophysical black holes is safely unaffected by ordinary galactic dark-matter environments.

The starting point of this work was an intriguing similarity between the behavior of fields near a degenerate horizon and near the infinity of an asymptotically flat spacetime, as revealed by the scattering theory for Dirac fields in the “exterior” region of the extreme Kerr–de Sitter black hole, developed by Borthwick. However, in that situation, the comparison was somewhat clouded by some of the analytical techniques used in intermediate steps of the proof. The aim of the present work is to clarify the comparison further by studying instead the peeling behavior of solutions to the wave equation at an extremal horizon. We focus first on the extreme Reissner–Nordström black hole, for which the Couch–Torrence inversion (a global conformal isometry that exchanges the horizon and infinity) makes the analogy explicit. Then, we explore more general spherically symmetric situations using the Couch–Torrence inversion outside of its natural context.

In this paper we complete a systematic study on quasinormal modes (QNMs) and late time tails for scalar, Dirac and Maxwell fields on a spherically symmetric Schwarzschild-like black hole with a global monopole in the Einstein-bumblebee theory. To look for QNMs, we solve the equations of motion for all perturbation fields considered herein numerically, by employing both the matrix and the WKB methods, and find good agreements for numeric data obtained by these two techniques in the regime when both are valid. The impact of the bumblebee parameter c , the monopole parameter η ^2, and the multipole number ℓ on the fundamental quasinormal frequency are analyzed in detail. Our results are shown in terms of the quasinormal frequency measured by $$\sqrt {1 + c} \,M$$ 1 + c M , where M is a black hole mass parameter. We observe, by increasing the parameter c ( η ^2) with fixed first few ℓ , that the real part of QNMs increases for all spin fields; while the magnitude of the imaginary part decreases for scalar and Dirac fields but increases for Maxwell fields. By increasing the multipole number ℓ with fixed other parameters, we disclose that the real part of QNMs for all spin fields increases while the magnitude of the imaginary part decreases for scalar and Dirac fields but increases for Maxwell fields. In the eikonal limit ( ℓ ≫ n ), QNMs for all spin fields coincide with each other and the real part scale linearly with ℓ . In particular, the asymptotic QNMs approach the corresponding results given by the first order WKB formula, and only the real part of QNMs is dependent on the bumblebee and monopole parameters. In addition, it is shown that the late time behavior is determined not only by the multipole number but also by the bumblebee and monopole parameters, and is distinct for bosonic and fermonic fields. Moreover, the presence of the bumblebee (monopole) field makes the spin fields decay faster. Our results indicate, both in the context of QNMs and late time tails, that the bumblebee field and the monopole field play the same role in determining the dynamic evolution of perturbation fields.

By employing an expansion in terms of the inverse multipole number, we derive analytic expressions for the quasinormal modes (QNMs) of scalar, Dirac and Maxwell perturbations in the Hayward black hole (BH) background. The metric has three interpretations: as a model for a radiating BH, as a quantum-corrected BH owing to the running gravitational coupling in the Asymptotically Safe Gravity, and as a BH solution in the Effective Field Theory. We show that the obtained compact analytical formulas approximate QNMs with remarkable accuracy for ℓ > 0.

Hawking initiated study of radiations from black holes. The black hole thermodynamics holds a significant importance in understanding of quantum nature of gravity. In this article, Hawking radiations have been studied by employing the semi-classical perspective of quantum tunneling. Dirac and Rarita-Schwinger equations have been employed to determine the tunneling probabilities of spin-1/2 and spin-3/2 particles, respectively, in the background of black holes developed in the asymptotically safe gravity. Hawking temperature determined in both cases is in agreement.

We define and analyze the fermionic entanglement entropy of a Schwarzschild black hole horizon for the regularized vacuum state of an observer at infinity. Using separation of variables and an integral representation of the Dirac propagator, the entanglement entropy is computed to be a prefactor times the number of occupied angular momentum modes on the event horizon.

Using the complete classification of the bases in the rotating black hole background we separate superradiance from the Hawking effect. We first find that there is spontaneous particle creation for fermions by the potential outside the black hole horizon for the frequencies inside the superradiant regime, i.e. $\omega<k\Omega_H$. However, these particles do not enhance the total flux from the black hole. For the superradiance particle to became real, its negative energy counterpart has to be canceled by the positive energy Hawking radiation mode at the horizon. Since due to the Pauli's principle this cancellation must be one-to-one, the superradiance effect cannot add anything to the total black hole flux. For an extremal black hole, the Hawking temperature is zero, horizon is not populated with thermal modes, and fermions can be emitted through the superradiance mechanism. On the other hand, a macroscopic flux of fermions infalling to the black hole is the opposite process of Hawking radiation. A positive energy-infalling particle must cancel out a negative energy thermal mode at the horizon, which leaves a net positive energy mode that crosses the horizon. Since there is finite thermal particle density at the horizon, this implies that there is a maximal fermion infalling rate which is also controlled by the Hawking temperature.

We study quasinormal modes of massive scalar and massless Dirac fields in the background of regular black holes and traversable wormholes arising in Covariant Effective Quantum Gravity. Using both the Jeffreys-Wentzel-Kramers-Brillouin approximation and time-domain integration, we analyze the impact of quantum corrections on the quasinormal spectra and late-time behavior of perturbations. Our results reveal the existence of slowly decaying, oscillatory tails and quasi-resonant modes in the scalar sector, particularly in the high-mass regime. In the fermionic case, the damping rate increases with the quantum correction parameter ξ, while the oscillation frequency decreases. We also observe pronounced echo-like structures in the time-domain profiles near the black hole-wormhole threshold. These findings provide insight into the dynamics of perturbations in quantum-corrected spacetimes and offer potential signatures for distinguishing black holes from wormholes in future gravitational wave observations.

No abstract available

In this paper, we explore the evolution of a Dirac oscillator (DO) field within the near-horizon region of the Banados, Teitelboim, and Zanelli (BTZ) black hole (BH) by seeking exact solutions to the corresponding DO equation. We obtain the relativistic frequency expression and analyze the impact of various parameters implicated in it. Our findings reveal that the damped mode of this fermionic oscillator field relies on the BH mass, spin of the fermionic field, and frequency of the oscillator field. Lastly, we focus on the quantum system for a zero oscillator frequency as a specific case and thoroughly analyze the obtained results.

Quasinormal modes for bosonic (scalar, electromagnetic, and axial gravitational) and fermionic field perturbations, radiated from black holes that carry quantum gravitational corrections at third order in the curvature to the Schwarzschild solution, are scrutinized from the propagation of analog transonic sound waves across a de Laval nozzle. The thermodynamic variables, the nozzle geometry, the Mach number, and the thrust coefficient are computed as functions of the parameter driving the effective action for quantum gravity containing a dimension-six local operator beyond general relativity. The quasinormal modes for quantum gravitational corrected analog black holes are also determined for higher overtones, yielding a more precise description of the quantum-corrected ringdown process and the gravitational waveform way before the fundamental mode sets in.

This work presents a comprehensive investigation of the gravitational phenomena that correspond to a non-commutative (NC) charged black hole, by incorporating NC geometry through a (r,θ) Moyal twist. We derive the deformed metric up to the second order of NC parameter Θ, utilizing the Seiberg–Witten map for Reissner–Nordström black hole. We explore how non-commutativity modifies key thermodynamic properties, such as the Hawking temperature and heat capacity, and the existence of a remnant mass at the final stage of the evaporation. Additionally, the study of Hawking radiation for bosonic and fermionic particles is discussed. Applying a perturbative method, scalar quasinormal modes are analyzed numerically. Furthermore, null geodesics and photon sphere stability are explored via curvature and topological methods. The shadow radius and deflection angle are computed to understand observational signatures. Lensing observables are compared to Event Horizon Telescope observations to provide probable constraints on the non-commutativity parameter. This study bridges theoretical predictions with astrophysical observations, offering insights into quantum gravity effects on black hole physics.

We investigate shadows, deflection angle, quasinormal modes (QNMs), and sparsity of Hawking radiation of the Schwarzschild string cloud black hole’s solution after applying quantum corrections required by the Generalised Uncertainty Principle (GUP). First, we explore the shadow’s behaviour in the presence of a string cloud using three alternative GUP frameworks: linear quadratic GUP (LQGUP), quadratic GUP (QGUP), and linear GUP. We then used the weak field limit approach to determine the effect of the string cloud and GUP parameters on the light deflection angle, with computation based on the Gauss–Bonnet theorem. Next, to compute the quasinormal modes of Schwarzschild string clouds incorporating quantum correction with GUP, we determine the effective potentials generated by perturbing scalar, electromagnetic and fermionic fields, using the sixth-order WKB approach in conjunction with the appropriate numerical analysis. Our investigation indicates that string and linear GUP parameters have distinct and different effects on QNMs. We find that the greybody factor increases due to the presence of string cloud while the linear GUP parameter shows the opposite. We then examine the radiation spectrum and sparsity in the GUP corrected black hole with the cloud of string framework, which provides additional information about the thermal radiation released by black holes. Finally, our inquiries reveal that the influence of the string parameter and the quadratic GUP parameter on various astrophysical observables is comparable, however the impact of the linear GUP parameter is opposite.

We study the propagation of massless fermionic fields, implementing a family of special functions: Heun functions, in solving the wave equation in three three-dimensional backgrounds, including the BTZ black hole in string theory and Lifshitz black hole solutions in conformal gravity and Hu–Sawicki F(R) theory. The main properties of the selected black hole solutions is that their line elements are Weyl related to that of a homogeneous spacetime, whose spatial part possesses Lie symmetry, described by Lobachevsky-type geometry with arbitrary negative Gaussian curvature. Using the Weyl symmetry of massless Dirac action, we consider the perturbation equations of fermionic fields in relation to those of the homogeneous background, which having definite singularities, are transformed into Heun’s equation. We point out the existence of quasinormal modes labeled by the accessory parameter of the Heun function. The distribution of the quasinormal modes has been clarified to satisfy the boundary conditions that require ingoing and decaying waves at the event horizon and conformal infinity, respectively. It turned out that the procedure based on the Heun function, beside reproducing the previously known results obtained via hypergeometric function for the BTZ and Lifshitz black hole solution in conformal gravity, brings up new families of quasinormal frequencies, which can also contain purely imaginary modes. Also, the analysis of the quasinormal modes shows that with the negative imaginary part of complex frequencies ω=ωRe+iωIm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega =\omega _{Re}+i\omega _{Im}$$\end{document}, the fermionic perturbations are stable in this background.

We study the greybody factors, quasinormal modes, and shadow of the higher dimensional de-Sitter (dS)/anti de-Sitter (AdS) black hole spacetimes derived from the Einstein-bumblebee gravity theory within the Lorentz symmetry breaking (LSB) framework. We specifically apply the semi-analytical WKB method and the time domain approach to study the scalar and Dirac perturbations of the black hole. In-depth researches are done on the effects of the LSB and dimensionality on the bosonic/fermionic greybody factors, quasinormal modes, and shadow of the higher dimensional bumblebee black hole. The results obtained are discussed, tabulated, and illustrated graphically.

Motivated by the connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators, we study the pole-skipping phenomena for rotating BTZ black holes. In particular, we investigate the effect of rotations on the pole-skipping point for various fields with spin s = 1/2, 1, 2/3, extending the previous research for s = 0, 2. We derive an analytic full tower of the pole-skipping points of fermionic (s = 1/2) and vector (s = 1) fields by the exact holographic Green’s functions. For the non-extremal black hole, the leading pole-skipping frequency is ωleading = 2πiTh(s − 1 + νΩ)/(1 − Ω2) where Th is the temperature, Ω the rotation, and ν := (∆+ − ∆−)/2, the difference of conformal dimensions (∆±). These are confirmed by another independent method: the near-horizon analysis. For the extremal black hole, we find that the leading pole-skipping frequency can occur at ωleadingextremal\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\omega}_{\textrm{leading}}^{\textrm{extremal}} $$\end{document} = −2πiTR(s + 1) only when ν = s + 1, where TR is the temperature of the right moving mode. It is non-trivial because it cannot be achieved by simply taking the extreme limit (Th → 0, Ω → 1) of the non-extremal black hole result.

In this study, we present a comprehensive analysis of a modified Frolov black hole (BH) model that incorporates two types of topological defects, a global monopole (GM) and a cloud of strings (CS). This composite BH solution is examined from multiple theoretical perspectives to explore the impact of these modifications on the BH’s geometric, thermodynamic and dynamical properties. We begin by studying the geometrical optics of the spacetime, focusing on the motion of null geodesics. Key features, such as the effective potential, photon sphere, the force acting on photons and the stability of circular photon orbits, are analyzed in detail. Our results show that the presence of GM and CS significantly affects the spacetime geometry and photon dynamics. In addition, the thermodynamic behavior of the modified BH is also investigated. We derive essential quantities such as the Hawking temperature and entropy, demonstrating how the inclusion of GM and CS leads to deviations from the standard thermodynamic relations observed in classical BH solutions. These deviations may offer valuable insights into quantum gravity and the role of topological defects in BH physics. Furthermore, we examine the BH shadow as an observational signature of the underlying geometry. Our analysis shows that the Frolov parameter tends to reduce the apparent size of the shadow, while the presence of topological defects, particularly GM and CS, enlarges it. In addition, we investigate the perturbative dynamics of the BH by studying both scalar (spin-0), fermionic (spin-1/2) and electromagnetic (spin-1) fields through the massless Klein–Gordon and Maxwell equations, respectively. Using the Wentzel–Kramers–Brillouin approximation, we compute the quasinormal modes (QNMs) for scalar and electromagnetic field perturbations. The results confirm the stability of the BH under small perturbations and show that the QNM frequencies and damping rates are strongly influenced by the Frolov parameter, electric charge, GM and CS.

In this work, we propose a new black hole solution, namely, a Hayward-like metric incorporating corrections due to non-commutativity by taking into account ∂ r ∧ ∂ θ Moyal twist. We begin by deriving this solution using the non-commutative gauge theory framework. The general properties of the metric are then analyzed, including the event horizon structure and the Kretschmann scalar. Analogous to the standard Hayward solution, the modified black hole remains regular, provided that additional dependence on the angle θ. Next, we examine the thermodynamic properties, computing the Hawking temperature, entropy, and heat capacity. From the temperature profile, we verify that there is no physical remnant mass when T (Θ,l) → 0, indicating a complete evaporation process. Quantum radiation is analyzed by considering both bosonic and fermionic particle modes, with an estimation of the particle creation density provided for each case. The effective potential is evaluated perturbatively to accomplish the analysis of quasinormal modes and the time-domain response for scalar perturbations. The study of null geodesics is explored to enable the characterization of the photon sphere and black hole shadows. Furthermore, the Gaussian curvature is determined to assess the stability of critical orbits, followed by an analysis of gravitational lensing using the Gauss-Bonnet theorem. Finally, the constraints (bounds) on the parameters Θ (non-commutativity) and l (“Hayward parameter”) are derived based on solar system tests, including the perihelion precession of Mercury, light deflection, and the Shapiro time delay effect.

We discuss the corrected thermodynamics and naked singularity structure of the topological static spherically symmetric solution in F(R,G) - gravity coupled with Born-Infeld—like nonlinear electrodynamics. Solutions admitting black holes with constant topological Euler density is analyzed in view of various thermodynamical variables. The inclusion of logarithmic correction to the entropy is extended to the other thermodynamical variables and the contribution of corrected variables are displayed on various plots. The stability of black hole under the effect of thermal variables is also studied. As a second scope of this study, solutions admitting timelike naked singularity are probed with bosonic and fermionic quantum wave packets to see if the singularity is quantum mechanically regular or not. In this context, the evolution of these probes remains well-defined if the corresponding spatial Hamiltonian operator is essentially self-adjoint. Our calculations reveal that when the singularity is probed with specific wave modes involving spin—0 and spin—1/2 quantum wave packets, the corresponding wave operators turn out to be essentially self-adjoint, which in turn implies unique well-defined time evolution.

In this work, we analyze the impact of non-metricity on particle creation and the evaporation process of black holes within the framework of bumblebee gravity. In general lines, we compare black holes in the metric formalism [1] and the metric-affine approach [2]. Initially, we focus on bosonic particle modes to investigate Hawking radiation. Using the Klein-Gordon equation, we compute the Bogoliubov coefficients and derive the Hawking temperature. Subsequently, we examine Hawking radiation as a tunneling process, resolving divergent integrals through the residue method. The analysis is then extended to fermionic particle modes, also within the tunneling framework. Particle creation densities are calculated for both bosonic and fermionic cases. Additionally, greybody bounds are estimated for bosonic and fermionic particles. Furthermore, we explore the evaporation process, considering the final state of the black holes and we also investigate the correlation between the greybody factors and the quasinormal modes. Finally, constraints on the Lorentz-violating parameters ℓ (for the metric case) and X (for the metric-affine case) are established using recent astrophysical data on black hole lifetimes. In a general panorama, non-metricity (except for the tensor perturbations) in bumblebee gravity raises particle density for bosons while reducing it for fermions, increases greybody factors (for both bosons and fermions), amplifies the emission rate, and accelerates the evaporation process.

In a relativistic framework, it is generally accepted that quantum steering of maximally entangled states provide greater advantages in practical applications compared to non-maximally entangled states. In this paper, we investigate quantum steering for four different types of Bell-like states of fermionic modes near the event horizon of a Schwarzschild black hole. In some parameter spaces, the peak of steering asymmetry corresponds to a transition from two-way to one-way steerability for Bell-like states under the influence of the Hawking effect. It is intriguing to find that the fermionic steerability of the maximally entangled states experiences sudden death with the Hawking temperature, while the fermionic steerability of the non-maximally entangled states maintains indefinite persistence at infinite Hawking temperature. In contrast to prior research, this finding suggests that quantum steering of non-maximally entangled states is more advantageous than that of maximally entangled states for processing quantum tasks in the gravitational background. This surprising result overturns the traditional idea of ``the advantage of maximally entangled steering in the relativistic framework"and provides a new perspective for understanding the Hawking effect of the black hole.

We investigate quantum chaotic features of the brickwall model, which is obtained by introducing a stretched horizon — a Dirichlet wall placed outside the event horizon — within the BTZ geometry. This simple yet effective model has been shown to capture key properties of quantum black holes and is motivated by the stringy fuzzball proposal. We analyze the dynamics of both scalar and fermionic probe fields, deriving their normal mode spectra with Gaussian-distributed boundary conditions on the stretched horizon. By interpreting these normal modes as energy eigenvalues, we examine spectral statistics, including level spacing distributions, the spectral form factor, and Krylov state complexity as diagnostics for quantum chaos. Our results show that the brickwall model exhibits features consistent with random matrix theory across various ensembles as the standard deviation of the Gaussian distribution is varied. Specifically, we observe Wigner-Dyson distributions, a linear ramp in the spectral form factor, and a characteristic peak in Krylov complexity, all without the need for a classical interior geometry. We also demonstrate that non-vanishing spectral rigidity alone is sufficient to produce a peak in Krylov complexity, without requiring Wigner-Dyson level repulsion. Finally, we identify signatures of integrability at extreme values of the Dirichlet boundary condition parameter.

We show that the thermal radiation derived by Hawking can be smoothly extended to the T=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T=0$$\end{document} limit for Kerr black holes. The emission of the modes with ω>mΩ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega > m\varOmega $$\end{document} comes to a halt as the surface gravity vanishes. However, Kerr black holes smoothly continue to radiate both in bosonic and fermionic modes with ω<mΩ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega < m\varOmega $$\end{document}, at the T=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T=0$$\end{document} limit. We derive explicit expressions for the absorption probabilities which imply that the highest rate of emission pertains to the modes with ω=(mΩ)/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega =(m\varOmega )/2$$\end{document}, both for bosonic and fermionic cases. At the zero limit of thermal radiation, the number of emitted particles vanishes as ω→0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega \rightarrow 0$$\end{document}, which strictly differentiates it from the non-thermal radiation of soft particles by extremal Kerr black holes. We also note that the thermal radiation at the zero limit, drives the black hole away from extremality in accord with the third law and the cosmic censorship conjecture.

We study fermionic modes localized on the static spherically symmetric self-gravitating non-Abelian monopole in the $SU(2)$ Einstein-Dirac-Yang-Mills-Higgs theory. We consider dependence of the spectral flow on the effective gravitational coupling constant and show that, in the limiting case of transition to the Reissner-Nordstr\"{o}m black hole, the fermion modes are fully absorbed into the interior of the black hole.

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static nonrotating black holes, corresponding to the Schwarzschild, Reissner-Nordström, and extreme Reissner-Nordström solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress energy differs even in sign from the analytic approximation. For the Reissner-Nordström and extreme Reissner-Nordström solutions, divergences predicted by the analytic approximations are shown not to exist.

This paper studies a rotating Kiselev black hole surrounded by dark energy, whose spacetime metric is a solution to the Einstein field equations. Quintessence is a scalar field with negative pressure, related to the state parameter ω of the dark energy surrounding this black hole. Based on Lorentz-breaking, WKB approximation theory, and quantum tunneling radiation theory, we investigate the characteristic of quantum tunneling radition of spin-1/2 fermions and the result of the correction entropy in this special type of black hole. Additionally, we explore the significance of new expressions for physical quantities such as the Hawking temperature and Bekenstein–Hawking entropy of this black hole.

We analyze the analytic structure of correlators in the field theory dual to the quantum Bañados-Teitelboim-Zanelli (qBTZ) black hole, a braneworld model incorporating exact backreaction from quantum conformal matter. We first compute the quasi-normal mode (QNM) spectrum of operators with dimension ∆ and spin s = 0, ±1/2. The leading QNMs and their overtones display qualitatively different behavior depending on the branch of qBTZ solution, which corresponds to distinct CFT states: branch 1 is a conical singularity dressed with a horizon while branch 2 is a quantum-corrected BTZ black hole. Consequently, the relaxation of probe matter effectively differentiates the CFT states and identifies the corresponding bulk descriptions. We then turn to pole-skipping locations where Green’s functions are not unique. At these points, frequency is proportional to temperature, but momentum exhibits complex temperature dependence due to quantum effects. Under the assumption that the pole-skipping point closest to the origin reflects quantum chaos, we infer the likely behavior of the quantum Lyapunov exponent and butterfly velocity in the dual theory. Finally, we examine pole collisions in complex momentum space, showing that quantum corrections imprint a unique signature on the analytic structure of the poles in retarded Green’s functions, resulting in level-crossing phenomena that differ notably from the level-touching phenomena in the uncorrected BTZ geometry.

We calculate the quasinormal modes of a nonsingular spherically symmetric black hole effective model with holonomy corrections. The model is based on quantum corrections inspired by loop quantum gravity. It is covariant and results in a spacetime that is regular everywhere with a parameter-dependent black bounce. Perturbations of these black holes due to massless scalar and electromagnetic fields have been previously calculated and some intriguing results were observed. For some modes, the frequency versus minimum-radius parameter trajectories were found to spiral and self-intersect in the complex plane. In addition, the spectrum of overtones has real frequencies that oscillate with increasing overtone number, and may even vanish for some overtones. We have calculated the quasinormal modes for all massless spin perturbations, including spin-1/2, and axial- and polar-gravitational. We find that the trajectory-spirals are restricted to scalar perturbations and observe some interesting overtone behaviour for gravitational perturbations. The amount of isospectrality violation in the gravitational quasinormal mode spectra is also examined.

In this paper we explore the properties of a 1-dimensional spin chain in the presence of chiral interactions, focusing on the system's transition to distinct chiral phases for various values of the chiral coupling. By employing the mean field theory approximation we establish a connection between this chiral system and a Dirac particle in the curved spacetime of a black hole. Surprisingly, the black hole horizon coincides with the interface between distinct chiral phases. We examine the chiral properties of the system for homogeneous couplings and in scenarios involving position dependent couplings that correspond to black hole geometries. To determine the significance of interactions in the chiral chain we employ bosonization techniques and derive the corresponding Luttinger liquid model. Furthermore, we investigate the classical version of the model to understand the impact of the chiral operator on the spins and gain insight into the observed chirality. Our findings shed light on the behavior of the spin chain under the influence of the chiral operator, elucidating the implications of chirality in various contexts, including black hole physics.

Considering the Lorentz breaking theory, the correct modified forms of the dynamic equations of bosons and fermions in curved space-time are studied. For the new form of fermions dynamic equation through spin 1/2 Dirac particles in the black hole space-time in gravity’s rainbow, by introducing aether-like vector field and correctly constructing gamma matrix, new meaningful expressions of Hawking temperature, tunneling rate and Bekenstein-Hawking entropy of this black hole are obtained. In addition, the distribution characteristics of the energy levels of Dirac particles are also studied, and meaningful results are obtained. The research results show that the Lorentz breaking terms will cause a certain degree of correction to the tunneling radiation of fermions in the curved space-time of the black hole.