Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2604.19848

Greybody Factor, Resonant Frequencies, and Entropy Quantization of Charged Scalar Fields in the Kerr-EMDA Black Hole

Nazım Sertkan, İzzet Sakallı

gr-qcastro-ph.HEhep-thquant-phSubmitted Apr 21, 2026• Announced Apr 22, 2026• Revised May 22, 2026 (v2)
v1 · Apr 21, 2026v2 · May 22, 2026
arXivHTMLPDF

Abstract

We study charged massive scalar field perturbations on the rotating black hole (BH) background of Einstein-Maxwell-Dilaton-Axion (EMDA) theory, known as the Kerr-EMDA BH. Starting from the gauge-covariant Klein-Gordon equation (KGE), we perform a full separation of variables and obtain exact analytical solutions for both the angular and radial parts in terms of confluent Heun functions (CHFs). Unlike the earlier neutral scalar treatment by Senjaya and Ponglertsakul [Eur. Phys. J. C \textbf{85}, 352 (2025)], the electromagnetic coupling $q$ fundamentally alters the structure of the Heun parameters and produces qualitatively new physics. Applying the CHF polynomial condition, we derive the resonant frequency spectrum whose imaginary parts are equispaced with $|Δω_I| = 1/(2M)$, a universal spacing determined solely by the BH mass. Via the Maggiore prescription and the first law of BH thermodynamics, this yields a parameter-dependent entropy quantum $δS_{\text{BH}} = 4πr_+/(r_+ - r_-)$, which reduces to $4π$ for Schwarzschild but diverges at extremality -- {\color{black}in contrast to the universal $2π$ obtained for the rotating linear dilaton BH (RLDBH).} We construct the effective potential governing scalar wave scattering and analyze its dependence on the dilaton parameter $D$, rotation $a$, and scalar charge $q$. In the massless uncharged limit, the CHF reduces to the Gauss hypergeometric function, {\color{black}enabling us to compute the first analytical greybody factor (GF) for the Kerr-EMDA geometry; we show that this reduction extends to massless charged scalars, yielding a closed-form GF that captures superradiant amplification.} We examine how the dilaton deformation distinguishes the Kerr-EMDA spectrum from the standard Kerr and Kerr-Newman cases.

Comments
38 pages, 8 figures, 5 tables. Revised version: To appear in EPJC. We thank R. A. Konoplya, A. Zhidenko, and E. dos Santos Costa Filho for pointing out relevant references and valuable comments

Related papers

Impact of nonlinear electrodynamics on quasinormal modes of rotating black strings

F. S. Mirekhtiary, I. Sakalli

We study massless scalar perturbations of rotating anti-de Sitter black strings sourced by a power-Maxwell field with negative exponent $s$. The charge enters the metric function as $-Qr^{p}$ with $p=2/(1-2s)$, and the case $s=-1/2$ gives a linear term with an algebraic horizon. Since rotation is a local boost of the static string, the rotating spectrum follows exactly from the static one evaluated at a frequency-dependent momentum. We compute the spectrum with the Horowitz-Hubeny series, Chebyshev collocation and time-domain evolution, each implemented in two independent codes and checked against the planar Schwarzschild-AdS limit. The charge acts in two ways. At the reduced charge $\hat q_c=0.72626$ the least damped pair of modes meets on the imaginary axis, so more strongly charged strings ring down without oscillation, and at the endpoint of the branch the spectrum is exactly hypergeometric. At large transverse momentum the distance of the modes from the light cone grows as $k^{1/(1-4s)}$, replacing the $k^{-1/5}$ law of the neutral brane. Rotation continues the exceptional point into a line in the plane of charge and rotation, adds a purely damped axisymmetric tower, and never produces superradiant growth. A near-horizon estimate used earlier for this geometry misses all of these effects.

gr-qcCross-listedarXiv:2610.33309•Oct 27, 2026

Scalar quasinormal and quasibound states of weakly magnetized Ernst--Schwarzschild spacetime: a confluent-Heun Wronskian approach

Danilo S. Ferreira, Luis B. Castro

We study the quasinormal-mode and quasibound-state spectra of a massless scalar field in weakly magnetized Ernst--Schwarzschild spacetime. In the separated $O(B_0^2)$ regime, the Klein--Gordon equation reduces to a radial confluent-Heun equation. We construct an endpoint-selected spectral Wronskian directly from the canonical confluent-Heun recurrence and its regular-to-irregular connection limit. Quasinormal modes and quasibound states are then obtained as zeros of the same analytic spectral function on the radiative and bound sheets, respectively, providing a unified treatment of the two spectral sectors within the separated weak-field problem. The resulting QNM and QBS frequencies agree with independent weak-field Ernst and massive-Schwarzschild benchmarks available in the literature. We further show, for representative cases, that the frequencies selected by the local Heun-series termination relation examined here do not satisfy the endpoint-selected quasibound-state condition. The construction therefore provides a direct horizon-to-infinity spectral condition for both radiative and bound states within the weak-field Ernst problem.

gr-qcCross-listedarXiv:2609.17727•Sep 17, 2026

Massive quantum divergence on the Cauchy horizon of a black hole

Marc Casals, Lorenzo Pisani, Peter Taylor

We investigate a quantum massive scalar field in the interior of a charged and spherically-symmetric (Reissner-Nordström) black hole. We examine the behaviour for varying values of the black hole charge, field mass and coupling constant when the field is in two quantum states: Hartle-Hawking (representing a black hole in thermal equilibrium) and Unruh (representing a black hole evaporating via the emission of Hawking radiation). We show that the vacuum polarization as well as the angular components of the quantum stress-energy tensor diverge on the Cauchy horizon, in stark contrast to what happens for massless fields. We also calculate the energy fluxes in Eddington-Finkelstein coordinates $\{u,v\}$. We show that these fluxes on the Cauchy horizon do not generically vanish. This implies, in particular, that in regular, Kruskal coordinates $\{U,V\}$ the ingoing flux diverges like $V^{-2}$ on the Cauchy horizon (where $V=0$). This divergence suggests that its backreaction via the semiclassical Einstein equations would yield a strong singularity, as opposed to its weaker, classical counterpart. Interestingly, there are exceptions, in which the energy fluxes in Eddington-Finkelstein coordinates vanish: (i) in the extremal limit (where the black hole is maximally charged); (ii) certain fine-tuned regions of parameter space, where the fluxes change sign.

gr-qcCross-listedarXiv:2609.10755•Sep 11, 2026

A Covariant Chiral-Hydrodynamic Formulation of the Dirac Equation in Curved Spacetime

Jorge Meza-Domínguez, Tonatiuh Matos

The hydrodynamic formulation of the Dirac equation has historically been hindered by the inability to close the system of physical variables without resorting to infinite moment hierarchies. We resolve this longstanding issue by developing a fully covariant chiral-hydrodynamic formulation of the Dirac field in curved spacetime. Working in the Weyl representation, we introduce two independent null vectors, $P_L^μ$ and $P_R^μ$, which decouple the left and right chiral components. This allows us to define chiral geodesic and stochastic velocities, yielding a closed system of exactly eight real equations that corresponds directly to the Dirac field degrees of freedom. Remarkably, this formulation naturally isolates the spin-orbit coupling $(q/2)σ^{μν}F_{μν}$ while demonstrating the vanishing of the spin-gravity coupling in torsion-free general relativity. To demonstrate the analytical power of this framework, we specialize to the Schwarzschild geometry. We obtain exact radial solutions in terms of confluent Heun functions and directly compute the quasi-bound state spectrum (fermionic resonances), quasinormal mode frequencies, and greybody factors. Furthermore, by establishing an exact energy balance equation -- representing the first law of thermodynamics for Dirac fields -- we derive the Hawking radiation flux purely from chiral flux conservation at the event horizon. This work not only provides a closed hydrodynamic theory for spin-1/2 fluids but also establishes a unified framework for analyzing quantum information and fermion dynamics in strong gravitational backgrounds.

gr-qcCross-listedarXiv:2605.28887•May 28, 2026

Scalar-Tensor Gravity as a Probe of Generalized Black Hole Entropy

Hussain Gohar

We develop a geometric realization of a broad class of generalized black hole entropy functionals by establishing their direct correspondence with the Misner$-$Sharp quasilocal mass and the Wald Noether$-$charge entropy in scalar$-$tensor theories of gravity. The resulting models feature a scale-dependent effective gravitational coupling, whose functional dependence is determined by the underlying entropy parameters. Within this framework, we derive explicit Einstein-frame scalar potentials: for Barrow entropy, a steep exponential potential; for Tsallis$-$Cirto entropy, an exponential potential governed by the nonextensivity parameter; and for quantum-gravity and entanglement$-$induced corrections, an approximately linear potential. These distinct potentials generate characteristic cosmological phenomenology, with implications for inflationary dynamics, late-time dark-energy behavior, and non-singular bouncing cosmologies. The framework is compatible with current constraints from solar-system tests, big-bang nucleosynthesis, and pulsar-timing observations, and it yields predictions that can be probed by forthcoming observational surveys. In this way, the analysis establishes a unified and geometrically grounded connection between information$-$theoretic entropy proposals and gravitational field theory.

gr-qcCross-listedarXiv:2605.18551•May 19, 2026

Finite Hilbert space and maximum mass of Schwarzschild black holes from a Generalized Uncertainty Principle

S. Jalalzadeh, H. Moradpour

We show that implementing a generalized uncertainty principle (GUP) with both minimal length and maximal momentum directly on the reduced phase space of the Schwarzschild black hole (BH) leads to a finite and discrete mass spectrum, a strict upper bound on the BH mass, a bounded entropy, and a fully regulated Hawking temperature. We further construct a GUP-deformed lapse function that preserves the ADM mass and horizon radius while exactly reproducing the GUP temperature through the surface gravity. Using the most massive observed supermassive BHs, we derive the constraint on the GUP parameter, $β\lesssim 10^{-98}$, showing that present astrophysical data already impose robust bounds on minimal length quantum gravity.

gr-qcCross-listedarXiv:2604.08953•Apr 13, 2026
We study charged massive scalar field perturbations on the rotating black hole (BH) background of Einstein-Maxwell-Dilaton-Axion (EMDA) theory, known as the Kerr-EMDA BH. Starting from the gauge-covariant Klein-Gordon equation (KGE), we perform a full separation of variables and obtain exact analytical solutions for both the angular and radial parts in terms of confluent Heun functions (CHFs). Unlike the earlier neutral scalar treatment by Senjaya and Ponglertsakul [Eur. Phys. J. C \textbf{85}, 352 (2025)], the electromagnetic coupling qqq fundamentally alters the structure of the Heun parameters and produces qualitatively new physics. Applying the CHF polynomial condition, we derive the resonant frequency spectrum whose imaginary parts are equispaced with ∣ΔωI∣=1/(2M)|Δω_I| = 1/(2M)∣ΔωI​∣=1/(2M), a universal spacing determined solely by the BH mass. Via the Maggiore prescription and the first law of BH thermodynamics, this yields a parameter-dependent entropy quantum δSBH=4πr+/(r+−r−)δS_{\text{BH}} = 4πr_+/(r_+ - r_-)δSBH​=4πr+​/(r+​−r−​), which reduces to 4π4π4π for Schwarzschild but diverges at extremality -- {\color{black}in contrast to the universal 2π2π2π obtained for the rotating linear dilaton BH (RLDBH).} We construct the effective potential governing scalar wave scattering and analyze its dependence on the dilaton parameter DDD, rotation aaa, and scalar charge qqq. In the massless uncharged limit, the CHF reduces to the Gauss hypergeometric function, {\color{black}enabling us to compute the first analytical greybody factor (GF) for the Kerr-EMDA geometry; we show that this reduction extends to massless charged scalars, yielding a closed-form GF that captures superradiant amplification.} We examine how the dilaton deformation distinguishes the Kerr-EMDA spectrum from the standard Kerr and Kerr-Newman cases.
We study massless scalar perturbations of rotating anti-de Sitter black strings sourced by a power-Maxwell field with negative exponent sss. The charge enters the metric function as −Qrp-Qr^{p}−Qrp with p=2/(1−2s)p=2/(1-2s)p=2/(1−2s), and the case s=−1/2s=-1/2s=−1/2 gives a linear term with an algebraic horizon. Since rotation is a local boost of the static string, the rotating spectrum follows exactly from the static one evaluated at a frequency-dependent momentum. We compute the spectrum with the Horowitz-Hubeny series, Chebyshev collocation and time-domain evolution, each implemented in two independent codes and checked against the planar Schwarzschild-AdS limit. The charge acts in two ways. At the reduced charge q^c=0.72626\hat q_c=0.72626q^​c​=0.72626 the least damped pair of modes meets on the imaginary axis, so more strongly charged strings ring down without oscillation, and at the endpoint of the branch the spectrum is exactly hypergeometric. At large transverse momentum the distance of the modes from the light cone grows as k1/(1−4s)k^{1/(1-4s)}k1/(1−4s), replacing the k−1/5k^{-1/5}k−1/5 law of the neutral brane. Rotation continues the exceptional point into a line in the plane of charge and rotation, adds a purely damped axisymmetric tower, and never produces superradiant growth. A near-horizon estimate used earlier for this geometry misses all of these effects.
We study the quasinormal-mode and quasibound-state spectra of a massless scalar field in weakly magnetized Ernst--Schwarzschild spacetime. In the separated O(B02)O(B_0^2)O(B02​) regime, the Klein--Gordon equation reduces to a radial confluent-Heun equation. We construct an endpoint-selected spectral Wronskian directly from the canonical confluent-Heun recurrence and its regular-to-irregular connection limit. Quasinormal modes and quasibound states are then obtained as zeros of the same analytic spectral function on the radiative and bound sheets, respectively, providing a unified treatment of the two spectral sectors within the separated weak-field problem. The resulting QNM and QBS frequencies agree with independent weak-field Ernst and massive-Schwarzschild benchmarks available in the literature. We further show, for representative cases, that the frequencies selected by the local Heun-series termination relation examined here do not satisfy the endpoint-selected quasibound-state condition. The construction therefore provides a direct horizon-to-infinity spectral condition for both radiative and bound states within the weak-field Ernst problem.
We investigate a quantum massive scalar field in the interior of a charged and spherically-symmetric (Reissner-Nordström) black hole. We examine the behaviour for varying values of the black hole charge, field mass and coupling constant when the field is in two quantum states: Hartle-Hawking (representing a black hole in thermal equilibrium) and Unruh (representing a black hole evaporating via the emission of Hawking radiation). We show that the vacuum polarization as well as the angular components of the quantum stress-energy tensor diverge on the Cauchy horizon, in stark contrast to what happens for massless fields. We also calculate the energy fluxes in Eddington-Finkelstein coordinates {u,v}\{u,v\}{u,v}. We show that these fluxes on the Cauchy horizon do not generically vanish. This implies, in particular, that in regular, Kruskal coordinates {U,V}\{U,V\}{U,V} the ingoing flux diverges like V−2V^{-2}V−2 on the Cauchy horizon (where V=0V=0V=0). This divergence suggests that its backreaction via the semiclassical Einstein equations would yield a strong singularity, as opposed to its weaker, classical counterpart. Interestingly, there are exceptions, in which the energy fluxes in Eddington-Finkelstein coordinates vanish: (i) in the extremal limit (where the black hole is maximally charged); (ii) certain fine-tuned regions of parameter space, where the fluxes change sign.
The hydrodynamic formulation of the Dirac equation has historically been hindered by the inability to close the system of physical variables without resorting to infinite moment hierarchies. We resolve this longstanding issue by developing a fully covariant chiral-hydrodynamic formulation of the Dirac field in curved spacetime. Working in the Weyl representation, we introduce two independent null vectors, PLμP_L^μPLμ​ and PRμP_R^μPRμ​, which decouple the left and right chiral components. This allows us to define chiral geodesic and stochastic velocities, yielding a closed system of exactly eight real equations that corresponds directly to the Dirac field degrees of freedom. Remarkably, this formulation naturally isolates the spin-orbit coupling (q/2)σμνFμν(q/2)σ^{μν}F_{μν}(q/2)σμνFμν​ while demonstrating the vanishing of the spin-gravity coupling in torsion-free general relativity. To demonstrate the analytical power of this framework, we specialize to the Schwarzschild geometry. We obtain exact radial solutions in terms of confluent Heun functions and directly compute the quasi-bound state spectrum (fermionic resonances), quasinormal mode frequencies, and greybody factors. Furthermore, by establishing an exact energy balance equation -- representing the first law of thermodynamics for Dirac fields -- we derive the Hawking radiation flux purely from chiral flux conservation at the event horizon. This work not only provides a closed hydrodynamic theory for spin-1/2 fluids but also establishes a unified framework for analyzing quantum information and fermion dynamics in strong gravitational backgrounds.
We develop a geometric realization of a broad class of generalized black hole entropy functionals by establishing their direct correspondence with the Misner−-−Sharp quasilocal mass and the Wald Noether−-−charge entropy in scalar−-−tensor theories of gravity. The resulting models feature a scale-dependent effective gravitational coupling, whose functional dependence is determined by the underlying entropy parameters. Within this framework, we derive explicit Einstein-frame scalar potentials: for Barrow entropy, a steep exponential potential; for Tsallis−-−Cirto entropy, an exponential potential governed by the nonextensivity parameter; and for quantum-gravity and entanglement−-−induced corrections, an approximately linear potential. These distinct potentials generate characteristic cosmological phenomenology, with implications for inflationary dynamics, late-time dark-energy behavior, and non-singular bouncing cosmologies. The framework is compatible with current constraints from solar-system tests, big-bang nucleosynthesis, and pulsar-timing observations, and it yields predictions that can be probed by forthcoming observational surveys. In this way, the analysis establishes a unified and geometrically grounded connection between information−-−theoretic entropy proposals and gravitational field theory.
We show that implementing a generalized uncertainty principle (GUP) with both minimal length and maximal momentum directly on the reduced phase space of the Schwarzschild black hole (BH) leads to a finite and discrete mass spectrum, a strict upper bound on the BH mass, a bounded entropy, and a fully regulated Hawking temperature. We further construct a GUP-deformed lapse function that preserves the ADM mass and horizon radius while exactly reproducing the GUP temperature through the surface gravity. Using the most massive observed supermassive BHs, we derive the constraint on the GUP parameter, β≲10−98β\lesssim 10^{-98}β≲10−98, showing that present astrophysical data already impose robust bounds on minimal length quantum gravity.