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.
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) 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 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 ∣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−), 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.
We study black-hole quasinormal modes by applying the complex scaling method (CSM) to the perturbation equations of Schwarzschild and Reissner--Nordström black holes. The method converts the outgoing-wave boundary condition into a non-Hermitian eigenvalue problem, allowing quasinormal-mode frequencies to be computed within a common spectral framework. We first benchmark the method for the Schwarzschild Regge--Wheeler equation and then extend it to the Reissner--Nordström family, including the extremal limit. Our results show that CSM provides a unified and flexible approach to the computation of black-hole quasinormal frequencies.
We apply the complex scaling method to black-hole perturbations in four-dimensional Schwarzschild--de~Sitter (dS) spacetimes. The method converts the outgoing-wave boundary-value problem into a non-Hermitian spectral problem and enables quasinormal-mode poles and the rotated continuum to be treated in a common framework. We focus in particular on the continuum level density, which characterizes the continuum response beyond isolated quasinormal-mode frequencies. Using Regge--Wheeler-type perturbation equations for scalar, electromagnetic, and gravitational fields, we investigate how a nonzero cosmological constant modifies the pole and continuum sectors. We also discuss a possible extension to string-inspired coupled-channel systems, and illustrate that higher-dimensional dS black holes can be treated within the same framework, at least in tensor- and vector-type sectors. Our results indicate that complex scaling offers a useful spectral framework for analyzing both quasinormal modes and continuum response in black-hole physics.
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, PLμ and PRμ, 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 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 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 −Qrp 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 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 k1/(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.
Non-Hermitian PT symmetric Klein-Gordon fields in Lorentz-violating wormholes spacetime background
We investigate a PT-symmetric Klein--Gordon (KG) oscillator in a (3+1)-dimensional Lorentz-violating (LV) traversable wormhole spacetime. The geometry is characterized by a smooth throat of radius a and a constant lapse function, A(x)=1, so that no Killing horizons occur and the two asymptotic regions at x→±∞ remain connected through the throat. The Lorentz violation modifies the radial geometry and the oscillator scale according to Ω=Ω/1−ζ. A nonminimal non-Hermitian coupling, Ft(x)=iΩx, leads to a PT-symmetric KG oscillator with a regular effective potential at the throat and a quadratic confinement at large ∣x∣. The radial equation can be mapped to the confluent Heun equation, and polynomial truncation gives a conditionally exactly solvable sector in which the oscillator frequency, throat radius, LV parameter, angular momentum, and radial quantum number satisfy algebraic constraints. For the degree-1 sector, these conditions restrict the allowed angular momenta and correlate them with the LV parameter. The resulting bound-state energies are real and discrete, with exact particle--antiparticle symmetry, E−=−E+, while the corresponding wave functions are regular and localized on the two-sided wormhole geometry. These results show how Lorentz violation and the PT-symmetric coupling modify the relativistic bound-state spectrum through the geometry of the wormhole.