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Alexander Zhidenko

Publications and source records attributed to Alexander Zhidenko.

At least 19 recordsLinked to original sources
arXiv2026

Ces\`aro convergence of the high-order WKB method and its applications to black-hole overtones and long-lived modes

We develop a fully automatic Mathematica implementation of the black-hole WKB method at very high orders based on the Bender-Wu algorithm, which in principle is limited only by memory and computational time, and show that when pushed to sufficiently high order and improved by diagonal Pad\'e approximants the method becomes efficient for two regimes which are usually regarded as difficult for the standard low-order WKB treatment: the first several overtones with n>l and the very long-lived quasinormal modes of massive fields. At the same time, we show that this efficiency has a nontrivial limitation: for black-hole metrics belonging to the non-moderate class, especially when higher coefficients of the near-horizon parametrization become large, the WKB sequence may exhibit an apparent convergence to values which are nevertheless far from the accurate quasinormal frequencies. Thus, numerical stabilization of the WKB output alone is not always a sufficient criterion of correctness. However, we observe that although the WKB method with diagonal or near-diagonal Pad\'e approximants does not exhibit monotonic convergence order by order, the corresponding Ces\`aro means become monotonically convergent once a sufficiently high WKB order is reached. This behavior may serve as an internal WKB criterion for the convergence of the method.

gr-qc↗
arXiv2026

An efficient higher-order WKB code for quasinormal modes and greybody factors

The higher-order WKB Mathematica code for computing quasinormal modes, whose accuracy was significantly enhanced through extensions to higher orders and, in particular, through the use of Padé resummation, has been widely employed in numerous studies over the past several years. In this work, we present an updated and optimized version of the code. The main improvement consists in expanding the effective potential in a Taylor series around its maximum, rather than evaluating the full analytic expression of the WKB formula for each specific potential. This modification leads to a substantial reduction in computation time. In cases where the effective potential is complicated and involves non-rational functions, the speed gain can reach several orders of magnitude, while preserving the accuracy of the method.

gr-qc↗
arXiv2025

Convergence of Higher-Curvature Expansions Near the Horizon: Hawking Radiation from Regular Black Holes

A recently proposed model incorporating a series of higher-curvature corrections allows for analytic black-hole solutions at each order of the expansion, with a fully regular black hole emerging in the limit of infinite number of terms. An important question that arises within this framework is how rapidly the series converges. For those classical observables, which are primarily determined by the geometry near the peak of the effective potential, it has been previously shown that the series converges remarkably fast, often within the first two orders. However, this rapid convergence does not extend to quantities such as Hawking radiation, which are highly sensitive to the geometry near the event horizon. Although each successive order yields a result that is significantly closer to that of the full infinite series, several terms are typically required to obtain a sufficiently accurate approximation of the regular black hole in this context.

gr-qc↗
arXiv2025

Time Evolution of Black Hole Perturbations in Quadratic Gravity

We study the full time-domain evolution of gravitational perturbations in black hole spacetimes arising in Einstein-Weyl gravity, a renormalizable extension of general relativity containing quadratic curvature corrections. We analyze both Schwarzschild and non-Schwarzschild solutions, focusing on monopole and higher multipole perturbations. Using semi-analytical methods based on the Rezzolla-Zhidenko parametrization for approximation of the black hole spacetime and time-domain integration for analysis of evolution of perturbations, we study the late-time behavior of gravitational perturbations. Our results show that the ringdown phase is followed by universal slowly decaying oscillatory tails with the envelope $ ψ\propto t^{-5/6} $. We also demonstrate the breakdown of the eikonal correspondence between quasinormal modes and unstable null geodesics, highlighting limitations of the WKB method in this context. Our analysis confirms the range of (in)stability of black holes in Einstein-Weyl gravity found in recent publications.

gr-qc↗
arXiv2025

Quasinormal Ringing and Shadows of Black Holes and Wormholes in Dark Matter-Inspired Weyl Gravity

Weyl gravity naturally generates effective dark matter and cosmological constant terms as integration constants, eliminating the need to explicitly introduce them into the theory. Additionally, the framework permits three intriguing solutions for compact objects: an asymptotically de Sitter Schwarzschild-like black hole described by the Mannheim-Kazanas solution, a non-Schwarzschild black hole, and a traversable wormhole that exists without exotic matter. In this work, we investigate the quasinormal spectra of all three solutions. We demonstrate that when the mass of the black hole corresponding to the Mannheim-Kazanas solution approaches zero, the perturbation equations yield an exact solution expressible through hypergeometric functions. The quasinormal modes of black holes in Weyl gravity can be classified into three distinct branches: Schwarzschild-like modes modified by effective dark matter and cosmological terms, and modes associated with empty spacetime (de Sitter and dark matter branches), which are further influenced by the black hole mass. Previous studies have shown that the dark matter term induces a secondary stage of quasinormal ringing following the initial Schwarzschild phase. Here, we compute the frequencies using convergent methods and elucidate how this unique time-domain behavior translates into the frequency domain. Furthermore, we demonstrate that the non-Schwarzschild black hole can be distinguished from both the Schwarzschild-like solution and the wormhole through their distinct quasinormal spectra. We also compute shadow radii for black holes and wormholes within Weyl gravity, revealing that wormholes with large throat radii can produce significantly smaller shadows compared to black holes of equivalent mass.

gr-qc↗
arXiv2020

Einstein-scalar-Gauss-Bonnet black holes: Analytical approximation for the metric and applications to calculations of shadows

Recently, numerical solutions to the field equations of Einstein-scalar-Gauss-Bonnet gravity that correspond to black-holes with non-trivial scalar hair have been reported. Here, we employ the method of the continued-fraction expansion in terms of a compact coordinate in order to obtain an analytical approximation for the aforementioned solutions. For a wide variety of coupling functionals to the Gauss-Bonnet term we were able to obtain analytical expressions for the metric functions and the scalar field. In addition we estimated the accuracy of these approximations by calculating the black-hole shadows for such black holes. Excellent agreement between the numerical solutions and analytical approximations has been found.

gr-qc↗
arXiv2018

Quasinormal modes of massive fermions in Kerr spacetime: Long-lived modes and the fine structure

Quasinormal modes of a massive Dirac field were calculated for various static black hole backgrounds with the help of the WKB formula. These estimations, however, are rough and valid only for very small values of $μM$, where $M$ and $μ$ are mass of the black hole and field respectively. Thus, no accurate calculations of massive Dirac modes are known even for the Schwarzschild black hole and this is all the more so for the Kerr solution. Here we calculate quasinormal modes of a massive Dirac field in the Kerr background. We have shown that the infinitely long-lived quasinormal modes (quasiresonances), which exist for boson fields, appear also in the fermions' quasinormal spectrum. Two chiralities of massive fermions lead to an additional "fine structure" in the spectrum. We discuss the effect of this fine structure on the behavior of quasiresonances and the stability. The analysis is also extended to a charged massive field in the Kerr-Newman background.

gr-qc↗
arXiv2016

A new method for shadow calculations: application to parameterised axisymmetric black holes

Collaborative international efforts under the name of the Event Horizon Telescope project, using sub- mm very long baseline interferometry, are soon expected to provide the first images of the shadow cast by the candidate supermassive black hole in our Galactic center, Sagittarius A*. Observations of this shadow would provide direct evidence of the existence of astrophysical black holes. Although it is expected that astrophysical black holes are described by the axisymmetric Kerr solution, there also exist many other black hole solutions, both in general relativity and in other theories of gravity, which cannot presently be ruled out. To this end, we present calculations of black hole shadow images from various metric theories of gravity as described by our recent work on a general parameterisation of axisymmetric black holes [R. Konoplya, L. Rezzolla and A. Zhidenko, Phys. Rev. D 93, 064015 (2016)]. An algorithm to perform general ray-tracing calculations for any metric theory of gravity is first outlined and then employed to demonstrate that even for extremal metric deformation parameters of various black hole spacetimes, this parameterisation is both robust and rapidly convergent to the correct solution.

gr-qc↗
arXiv2016

Detection of gravitational waves from black holes: Is there a window for alternative theories?

Recently LIGO and VIRGO collaborations reported about observation of gravitational-wave signal corresponding to the inspiral and merger of two black holes, resulting into formation of the final black hole. It was shown that the observations are consistent with the Einstein theory of gravity with high accuracy limited mainly by the statistical error. Angular momentum and mass of the final black hole were determined with rather large allowance of tens of percents. Here we shall show that this indeterminacy in the range of the black-hole parameters allows for some not negligible deformations of the Kerr spacetime leading to the same frequencies of black-hole ringing. This means that at the current precision of the experiment there remain some possibilities for alternative theories of gravity.

gr-qc↗
arXiv2016

General parametrization of axisymmetric black holes in metric theories of gravity

Following previous work of ours in spherical symmetry, we here propose a new parametric framework to describe the spacetime of axisymmetric black holes in generic metric theories of gravity. In this case, the metric components are functions of both the radial and the polar angular coordinates, forcing a double expansion to obtain a generic axisymmetric metric expression. In particular, we use a continued-fraction expansion in terms of a compactified radial coordinate to express the radial dependence, while we exploit a Taylor expansion in terms of the cosine of the polar angle for the polar dependence. These choices lead to a superior convergence in the radial direction and to an exact limit on the equatorial plane. As a validation of our approach, we build parametrized representations of Kerr, rotating dilaton, and Einstein-dilaton-Gauss-Bonnet black holes. The match is already very good at lowest order in the expansion and improves as new orders are added. We expect a similar behavior for any stationary and axisymmetric black-hole metric.

gr-qc↗
arXiv2014

New parametrization for spherically symmetric black holes in metric theories of gravity

We propose a new parametric framework to describe in generic metric theories of gravity the spacetime of spherically symmetric and slowly rotating black holes. In contrast to similar approaches proposed so far, we do not use a Taylor expansion in powers of M/r, where M and r are the mass of the black hole and a generic radial coordinate, respectively. Rather, we use a continued-fraction expansion in terms of a compactified radial coordinate. This choice leads to superior convergence properties and allows us to approximate a number of known metric theories with a much smaller set of coefficients. The measure of these coefficients via observations of near-horizon processes can be used to effectively constrain and compare arbitrary metric theories of gravity. Although our attention is here focussed on spherically symmetric black holes, we also discuss how our approach could be extended to rotating black holes.

gr-qc↗
arXiv2009

Linear perturbations of black holes: stability, quasi-normal modes and tails

Black holes have their proper oscillations, which are called the quasi-normal modes. The proper oscillations of astrophysical black holes can be observed in the nearest future with the help of gravitational wave detectors. Quasi-normal modes are also very important in the context of testing of the stability of black objects, the anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence and in higher dimensional theories, such as the brane-world scenarios and string theory. This dissertation reviews a number of works, which provide a thorough study of the quasi-normal spectrum of a wide class of black holes in four and higher dimensions for fields of various spin and gravitational perturbations. We have studied numerically the dependance of the quasi-normal modes on a number of factors, such as the presence of the cosmological constant, the Gauss-Bonnet parameter or the aether in the space-time, the dependance of the spectrum on parameters of the black hole and fields under consideration. By the analysis of the quasi-normal spectrum, we have studied the stability of higher dimensional Reissner-Nordstrom-de Sitter black holes, Kaluza-Klein black holes with squashed horizons, Gauss-Bonnet black holes and black strings. Special attention is paid to the evolution of massive fields in the background of various black holes. We have considered their quasi-normal ringing and the late-time tails. In addition, we present two new numerical techniques: a generalisation of the Nollert improvement of the Frobenius method for higher dimensional problems and a qualitatively new method, which allows to calculate quasi-normal frequencies for black holes, which metrics are not known analytically.

gr-qc↗
arXiv2008

Evolution of Brane-Localised Standard Model Fields in Gauss-Bonnet theory

We study the massless scalar, Dirac and electro-magnetic fields propagating on a 4D-brane, which is embedded in higher dimensional Gauss-Bonnet space-time. We calculate, in time-domain, the fundamental quasi-normal modes of a spherically symmetric black hole for such fields. We observe also a universal behavior, independent on a field and value of the Gauss-Bonnet parameter, at asymptotically late time.

gr-qc↗
arXiv2008

Evolution of perturbations of squashed Kaluza-Klein black holes: escape from instability

The squashed Kaluza-Klien (KK) black holes differ from the Schwarzschild black holes with asymptotic flatness or the black strings even at energies for which the KK modes are not excited yet, so that squashed KK black holes open a window in higher dimensions. Another important feature is that the squashed KK black holes are apparently stable and, thereby, let us avoid the Gregory-Laflamme instability. In the present paper, the evolution of scalar and gravitational perturbations in time and frequency domains is considered for these squashed KK black holes. The scalar field perturbations are analyzed for general rotating squashed KK black holes. Gravitational perturbations for the so called zero mode are shown to be decayed for non-rotating black holes, in concordance with the stability of the squashed KK black holes. The correlation of quasinormal frequencies with the size of extra dimension is discussed.

hep-th↗
arXiv2007

Quasi-normal modes for black hole solutions unknown in analytical form

We review the papers [1-3]. We discuss possibilities of studying the quasi-normal modes of black holes that are not known in an analytical form. Such black holes appear as solutions in various theoretical models and real astrophysical approximations when one takes into account the black hole neighborhood.

gr-qc↗
arXiv2006

Massive scalar field quasi-normal modes of higher dimensional black holes

We study quasinormal spectrum of massive scalar field in the $D$-dimensional black hole background. We found the qualitatively different dependence on the field mass of the fundamental modes for $D\geq6$. The behaviour of higher modes is qualitatively the same for all $D$. Thus for some particular values of mass (of the field and of the black hole) the spectrum has two dominating oscillations with a very long lifetime. Also we show that the asymptotically high overtones do not depend on the field mass. In addition, we present the generalisation of the Nollert improvement of the continued fraction technique for the numerical calculation of quasi-normal frequencies of $D$-dimensional black holes.

gr-qc↗