arXiv subjects

R. A. Konoplya

Publications and source records attributed to R. A. Konoplya.

At least 73 records · Page 4Linked to original sources

arXiv2020

Arbitrarily long-lived quasinormal modes in a wormhole background

Arbitrarily long lived modes, called quasi-resonances, are known to exist in the spectrum of massive fields for a number of black-hole backgrounds at some discrete values of mass of the field. Here we show that these modes also exist in the background of wormholes, unless a wormhole has a constant red-shift function, that is, tideless in the radial direction. The evidence of quasi-resonances is supported by calculations in the frequency and time domains, which are in a good concordance. At large masses of the field, time-domain profiles of the absolute value of the wave function have peculiar behavior: the long-lived modes dominate in the signal after a long period of power-law tails.

gr-qc↗

arXiv2019

Quantum corrected black holes: quasinormal modes, scattering, shadows

The spherically symmetric deformation of the Schwarzschild solution owing to the quantum corrections to gravity is known as Kazakov-Solodukhin black-hole metric. Neglecting non-spherical deformations of the background the problem was solved non-perturbatively. Here we analyze the basic characteristics of this geometry, such as: quasinormal modes and grey-body factors of fields of various spin and shadow cast by this black hole. The WKB approach and time-domain integration method, which we used for calculation of quasinormal modes, are in a good concordance. The analytical formula for quasinormal modes is deduced in the eikonal regime. The radius of shadow is decreasing when the quantum deformation is turned on.

gr-qc↗

arXiv2019

Stable Schwarzschild stars as black-hole mimickers

The Schwarzschild star is an ultracompact object beyond the Buchdahl limit, which has Schwarzschild geometry outside its surface and positive pressure in the external layer which vanishes at the surface. Recently it has been shown that the Schwarzschild star is stable against spherically symmetric perturbations. Here we study arbitrary axial nonspherical perturbations, and show that the observable quasinormal modes can be as close to the Schwarzschild limit as one wishes, what makes the Schwarzschild star a very good mimicker of a black hole. The decaying time-domain profiles prove that the Schwarzschild star is stable against nonspherical perturbations as well. Another peculiar feature is the absence of echoes at the end of the ringdown. Instead we observe a nonoscillating mode which might belong to the class of algebraically special modes. At asymptotically late times, Schwarzschildian power-law tails dominate in the signal.

gr-qc↗

arXiv2019

Analytical representation for metrics of scalarized Einstein-Maxwell black holes and their shadows

Here we construct approximate analytical forms for the metric coefficients and fields representing the scalarized Einstein-Maxwell black holes with various couplings of the scalar field, once the parameters of the system are fixed. By increasing approximation order, one can obtain the analytic representation with any desired accuracy, what was tested via calculations of shadows for these black holes by using approximate analytical and accurate numerical metric functions. We share the Mathematica code which allows one to find an appropriate analytical form of the metric for any couplings and values of parameters. Scalarization increases the radius of the black-hole shadow for all the considered coupling functions.

gr-qc↗

arXiv2019

Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations

The WKB approach for finding quasinormal modes of black holes, suggested in [1] by Schutz and Will at the first order and later developed to higher orders [2-4], became popular during the past decades, because, unlike more sophisticated numerical approaches, it is automatic for different effective potentials and mostly provides sufficient accuracy. At the same time, the seeming simplicity of the WKB approach resulted in appearance of a big number of partially misleading papers, where the WKB formula was used beyond its scope of applicability. Here we review various situations in which the WKB formula can or cannot bring us to reliable conclusions. As the WKB series converges only asymptotically, there is no mathematically strict criterium for evaluation of an error. Therefore, here we are trying to introduce a number of practical recipes instead and summarize cases in which higher WKB orders improve accuracy. We show that averaging of the Pade approximations, suggested first by J. Matyjasek and M. Opala [4], leads to much higher accuracy of the WKB approach, estimate the error and present the automatic code [5] which computes quasinormal modes and grey-body factors.

gr-qc↗

arXiv2019

Shadow of a black hole surrounded by dark matter

We consider a simple spherical model consisting of a Schwarzschild black hole of mass $M$ and a dark matter of mass $ΔM$ around it. The general formula for the radius of black-hole shadow has been derived in this case. It is shown that the change of the shadow is not negligible, once the effective radius of the dark matter halo is of order $\sim \sqrt{3 M ΔM}$. For this to happen, for example, for the galactic black hole, the dark matter must be concentrated near the black hole. For small deviations from the Schwarzschild limit, the dominant contribution into the size of a shadow is due to the dark matter under the photon sphere, but at larger deviations, the matter outside the photon sphere cannot be ignored.

gr-qc↗

arXiv2019

Quasinormal modes, scattering and Hawking radiation in the vicinity of Einstein-dilaton-Gauss-Bonnet black hole

Classical (quasinormal) and quantum (Hawking) radiations are investigated for test fields in the background of a four dimensional, spherically symmetric and asymptotically flat black hole in the Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The geometry of the EdGB black hole deviates from the Schwarzschild geometry only slightly. Therefore, here we observe that the quasinormal spectrum also deviates from its Schwarzschild limit at most moderately, allowing for a $9\%$ decrease in the damping rate and up to a $6\%$ decrease in the real oscillation frequency. However, the intensity of Hawking radiation of an electromagnetic field turned out to be much more sensitive characteristic than its quasinormal spectrum, allowing for a $54\%$ increase of the energy emission rate. The analytical formula for the eikonal regime of quasinormal modes is derived for test fields and it is shown that the correspondence between the eikonal quasinormal modes and null geodesics is indeed fulfilled for test fields, but is not expected for the gravitational one.

gr-qc↗

arXiv2019

Echoes of compact objects: new physics near the surface and matter at a distance

It is well known that a hypothetical compact object that looks like an Einsteinian (Schwarzschild or Kerr) black hole everywhere except a small region near its surface should have the ringdown profile predicted by the Einstein theory at early and intermediate times, but modified by the so-called echoes at late times. A similar phenomenon appears when one considers an Einsteinian black hole and a shell of matter placed at some distance from it, so that astrophysical estimates could be made for the allowed mass of the black hole environment. While echoes for both systems have been extensively studied recently, no such analysis has been done for a system featuring phenomena simultaneously, that is, echoes due to new physics near the surface/event horizon and echoes due to matter at some distance from the black hole. Here, following [9, 11], we consider a traversable wormhole obtained by identifying two Schwarzschild metrics with the same mass M at the throat, which is near the Schwarzschild radius, and add a nonthin shell of matter at a distance. This allows us to understand how the echoes of the surface of the compact object are affected by the astrophysical environment at a distance. The straightforward calculations for the time-domain profiles of such a system support the expectations that if the echoes are observed, they should most probably be ascribed to some new physics near the event horizon rather than some "environmental" effect.

gr-qc↗

arXiv2018

Massive nonminimally coupled scalar field in Reissner-Nordström spacetime: Long-lived quasinormal modes and instability

Here we show that the phenomenon of arbitrarily long-lived quasinormal modes (called quasiresonances) of a massive scalar field in the vicinity of a black hole is not an artifact of the test field approximation, but takes place also when the (derivative) coupling of a scalar field with the Einstein tensor is taken into consideration. We observe that at large coupling and high multipole numbers, the growing modes appear in the spectrum, which are responsible for the eikonal instability of the field. For small coupling, when the configuration is stable, there appear the purely imaginary quasinormal modes which are nonperturbative in the coupling constant. At the sufficiently small coupling the nonminimal scalar field is stable and the asymptotic late-time tails are not affected by the coupling term. The accurate calculations of quasinormal frequencies for a massive scalar field with the derivative coupling in the Reissner-Nordström black-hole background are performed with the help of Frobenius method, time-domain integration and WKB expansion.

gr-qc↗

arXiv2018

No stable wormholes in Einstein-dilaton-Gauss-Bonnet theory

In [P. Kanti, B. Kleihaus, J. Kunz, Phys. Rev. Lett. 107, 271101 (2011)] it was shown that the four-dimensional Einstein-dilaton-Gauss-Bonnet theory allows for wormholes without introducing any exotic matter. The numerical solution for the wormhole was obtained there and it was claimed that this solution is gravitationally stable against radial perturbations, what, by now, would mean the only known theoretical possibility for existence of an apparently stable, four-dimensional and asymptotically flat wormhole without exotic matter. Here, more detailed analysis of perturbations shows that the Kanti-Kleihaus-Kunz wormhole is unstable against small perturbations for any values of its parameters. The exponential growth appears in the time domain after a long period of damped oscillations, in the same way as it takes place in the case of unstable higher-dimensional black holes in the Einstein-Gauss-Bonnet theory. The instability is driven by the purely imaginary mode, which is nonperturbative in the Gauss-Bonnet coupling$α$.

gr-qc↗

arXiv2018

How to tell the shape of a wormhole by its quasinormal modes

Here we shall show how to reconstruct the shape function of a spherically symmetric traversable Lorenzian wormhole near its throat if one knows high frequency quasinormal modes of the wormhole. The wormhole spacetime is given by the Morris-Thorne ansatz. The solution to the inverse problem via fitting of the parameters within the WKB approach is unique for arbitrary tideless wormholes and some wormholes with non-zero tidal effects, but this is not so for arbitrary wormholes. As examples, we reproduce the near throat geometries of the Bronnikov-Ellis and tideless Morris-Thorne metrics by their quasinormal modes at high multipole numbers $\ell$.

gr-qc↗

arXiv2018

Axisymmetric black holes allowing for separation of variables in the Klein-Gordon and Hamilton-Jacobi equation

We determine the class of axisymmetric and asymptotically flat black-hole spacetimes for which the test Klein-Gordon and Hamilton-Jacobi equations allow for the separation of variables. The known Kerr, Kerr-Newman, Kerr-Sen and some other black-hole metrics in various theories of gravity are within the class of spacetimes described here. It is shown that although the black-hole metric in the Einstein-dilaton-Gauss-Bonnet theory does not allow for the separation of variables (at least in the considered coordinates), for a number of applications it can be effectively approximated by a metric within the above class. This gives us some hope that the class of spacetimes described here may be not only generic for the known solutions allowing for the separation of variables, but also a good approximation for a broader class of metrics, which does not admit such separation. Finally, the generic form of the axisymmetric metric is expanded in the radial direction in terms of the continued fractions and the connection with other black-hole parametrizations is discussed.

gr-qc↗

arXiv2018

Quasinormal behavior of the D-dimensional Schwarzshild black hole and higher order WKB approach

We study characteristic (quasinormal) modes of a $D$-dimensional Schwarzshild black hole. It proves out that the real parts of the complex quasinormal modes, representing the real oscillation frequencies, are proportional to the product of the number of dimensions and inverse horizon radius $\sim D r_{0}^{-1}$. The asymptotic formula for large multipole number $l$ and arbitrary $D$ is derived. In addition the WKB formula for computing QN modes, developed to the 3rd order beyond the eikonal approximation, is extended to the 6th order here. This gives us an accurate and economic way to compute quasinormal frequencies.

gr-qc↗

arXiv2018

Passage of radiation through wormholes of arbitrary shape

We study quasinormal modes and scattering properties via calculation of the $S$-matrix for scalar and electromagnetic fields propagating in the background of spherically and axially symmetric, traversable Lorentzian wormholes of a generic shape. Such wormholes are described by the Morris-Thorne ansatz and its axially symmetric generalization. The properties of quasinormal ringing and scattering are shown to be determined by the behavior of the wormhole's shape function $b(r)$ and shift factor $Φ(r)$ near the throat. In particular, wormholes with the shape function $b(r)$, such that $b'(r) \approx 1$, have very long-lived quasinormal modes in the spectrum. We have proved that the axially symmetric traversable Lorentzian wormholes, unlike black holes and other compact rotating objects, do not allow for superradiance. As a by product we have shown that the 6th order WKB formula used for scattering problems of black or wormholes provides high accuracy and thus can be used for quite accurate calculations of the Hawking radiation processes around various black holes.

hep-th↗

arXiv2017

Quasinormal modes of Gauss-Bonnet-AdS black holes: towards holographic description of finite coupling

Here we shall show that there is no other instability for the Einstein-Gauss-Bonnet-anti-de Sitter (AdS) black holes, than the eikonal one and consider the features of the quasinormal spectrum in the stability sector in detail. The obtained quasinormal spectrum consists from the two essentially different types of modes: perturbative and non-perturbative in the Gauss-Bonnet coupling $α$. The sound and hydrodynamic modes of the perturbative branch can be expressed through their Schwazrschild-AdS limits by adding a linear in $α$ correction to the damping rates: $ω\approx Re(ω_{SAdS}) - Im(ω_{SAdS}) (1 - α\cdot ((D+1) (D-4) /2 R^2)) i$, where $R$ is the AdS radius. The non-perturbative branch of modes consists of purely imaginary modes, whose damping rates unboundedly increase when $α$ goes to zero. When the black hole radius is much larger than the anti-de Sitter radius $R$, the regime of the black hole with planar horizon (black brane) is reproduced. If the Gauss-Bonnet coupling $α$ (or used in holography $λ_{GB}$) is not small enough, then the black holes and branes suffer from the instability, so that the holographic interpretation of perturbation of such black holes becomes questionable, as, for example, the claimed viscosity bound violation in the higher derivative gravity. For example, $D=5$ black brane is unstable at $|λ_{GB}|>1/8$ and has anomalously large relaxation time when approaching the threshold of instability.

hep-th↗

arXiv2017

An analytical approximation for the Einstein-dilaton-Gauss-Bonnet black hole metric

We construct an analytical approximation for the numerical black hole metric of P. Kanti, et. al. [PRD54, 5049 (1996)] in the four-dimensional Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The continued fraction expansion in terms of a compactified radial coordinate, used here, converges slowly when the dilaton coupling approaches its extremal values, but for a black hole far from the extremal state, the analytical formula has a maximal relative error of a fraction of one percent already within the third order of the continued fraction expansion. The suggested analytical representation of the numerical black hole metric is relatively compact and good approximation in the whole space outside the black hole event horizon. Therefore, it can serve in the same way as an exact solution when analyzing particles' motion, perturbations, quasinormal modes, Hawking radiation, accreting disks and many other problems in the vicinity of a black hole. In addition, we construct the approximate analytical expression for the dilaton field.

gr-qc↗

arXiv2017

Quasinormal modes of a scalar field in the Einstein--Gauss--Bonnet-AdS black hole background: Perturbative and non-perturbative branches

It has recently been found that quasinormal modes of asymptotically anti-de Sitter (AdS) black holes in theories with higher curvature corrections may help to describe the regime of intermediate 't Hooft coupling in the dual field theory. Here, we consider quasinormal modes of a scalar field in the background of spherical Gauss--Bonnet--anti-de Sitter (AdS) black holes. In general, the eigenvalues of wave equations are found here numerically, but at a fixed Gauss-Bonnet constant $α= R^2/2$ (where $R$ is the AdS radius), an exact solution of the scalar field equation has been obtained. Remarkably, the purely imaginary modes, which are usually appropriate only to some gravitational perturbations, were found here even for a test scalar field. These purely imaginary modes of the Einstein--Gauss--Bonnet theory do not have the Einsteinian limits, because their damping rates grow, when $α$ is decreasing. Thus, these modes are nonperturbative in $α$. The real oscillation frequencies of the perturbative branch are linearly related to their Schwarzschild-AdS limits $Re (ω_{GB}) = Re (ω_{SAdS}) (1+ K(D) (α/R^2))$, where $D$ is the number of spacetime dimensions. Comparison of the analytical formula with the frequencies found by the shooting method allows us to test the latter. In addition, we found exact solutions to the master equations for gravitational perturbations at $α=R^2/2$ and observed that for the scalar type of gravitational perturbations an eikonal instability develops.

gr-qc↗

arXiv2017

Are eikonal quasinormal modes linked to the unstable circular null geodesics?

In Phys. Rev. D 79, 064016 (2009) it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein-Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein-Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.

gr-qc↗