arXiv subjects

R. A. Konoplya

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

At least 37 records · Page 2Linked to original sources

arXiv2024

Two Regimes of Asymptotic Fall-off of a Massive Scalar Field in the Schwarzschild-de Sitter Spacetime

The decay behavior of a massless scalar field in the Schwarzschild-de Sitter spacetime is well-known to follow an exponential law at asymptotically late times $t \rightarrow \infty$. In contrast, a massive scalar field in the asymptotically flat Schwarzschild background exhibits a decay with oscillatory (sinusoidal) tails enveloped by a power law. We demonstrate that the asymptotic decay of a massive scalar field in the Schwarzschild-de Sitter spacetime is exponential. Specifically, if $μM \gg 1$, where $μ$ and $M$ represent the mass of the field and the black hole, respectively, the exponential decay is also oscillatory. Conversely, in the regime of small $μM$, the decay is purely exponential without oscillations. This distinction in decay regimes underscores the fact that, for asymptotically de Sitter spacetimes, a particular branch of quasinormal modes, instead of a "tail", governs the decay at asymptotically late times. There are two branches of quasinormal modes for the Schwarzschild-de Sitter spacetime: the modes of an asymptotically flat black hole corrected by a non-zero $Λ$-term, and the modes of an empty de Sitter spacetime corrected by the presence of a black hole. We show that the latter branch is responsible for the asymptotic decay. When $μM$ is small, the modes of pure de Sitter spacetime are purely imaginary (non-oscillatory), while at intermediate and large $μM$ they have both real and imaginary parts, what produces the two pictures of the asymptotic decay. In addition, we show that the asymptotic decay of charged and higher dimensional black hole is also exponential.

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arXiv2024

Overtones' outburst of asymptotically AdS black holes

Recently it was shown that small deformations of the asymptotically flat black-hole geometry in some region near its horizon which do not alter considerably the fundamental mode, nevertheless, strongly affect the first several (and higher) overtones which deviate at an increasing rate from their nondeformed limits. Here we show that, despite the quasinormal spectrum in anti-de Sitter (AdS) space is totally different from the asymptotically flat one, the outburst of overtones do take place at small near-horizon deformations of Schwarzschild-AdS spacetime as well. Moreover, qualitatively new, nonoscillatory modes appear as a result of such small deformations, representing, thereby, a nonperturbative branch of modes. For this purpose we extend the general parametrization of asymptotically flat black holes to the AdS case. Small near-horizon deformations may originate from various holographically motivated factors, such as quantum corrections or attempts to describe the regime of intermediate coupling via higher curvature terms, while the nonoscillatory modes may be related to the hydrodynamic mode on the gauge theory side. Therefore, the phenomenon of the overtones' outburst must be taken into consideration when analyzing correlation functions and dispersion relations in the dual field theory. In addition to the ad hoc deformations we consider the case of five-dimensional Einstein-Gauss-Bonnet-AdS black holes as an example of such near horizon deformations and fulfill the detailed study of the overtones.

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arXiv2023

The sound of the event horizon

During the ringdown phase of a gravitational signal emitted by a black hole, the least damped quasinormal frequency dominates. If modifications to Einstein's theory induce noticeable deformations of the black-hole geometry only near the event horizon, the fundamental mode remains largely unaffected. However, even a small change near the event horizon can significantly impact the first few overtones, providing a means to probe the geometry of the event horizon. Overtones are stable against small deformations of spacetime at a distance from the black hole, allowing the event horizon to be distinguished from the surrounding environment. In contrast to echoes, overtones make a much larger energy contribution. These findings open up new avenues for future observations.

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arXiv2023

Analytic expressions for quasinormal modes and grey-body factors in the eikonal limit and beyond

Although the WKB series converges only asymptotically and guarantees the exact result solely in the eikonal regime, we have managed to derive concise analytical expressions for the quasinormal modes and grey-body factors of black holes, expanding beyond the eikonal approximation. Remarkably, these expressions demonstrate unexpectedly strong accuracy. We suggest a comprehensive approach for deriving analytical expressions for grey-body factors and quasinormal modes at various orders beyond the eikonal approximation. Two cases are examined as examples: the Schwarzschild-de Sitter black hole and hairy black holes within the framework of Effective Field Theory. We have publicly shared a generic code that calculates analytical expressions for grey-body factors and quasinormal modes of spherical black holes.

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arXiv2023

General black-hole metric mimicking Schwarzschild spacetime

Using the general parametrization of spherically symmetric and asymptotically flat black holes in arbitrary metric theories of gravity and implying that: a) the post-Newtonian constraints are taken into account and b) basic astrophysically relevant characteristics (such as, dominant quasinormal modes, frequency at the innermost stable circular orbit, binding energy, radius of the shadow etc.) are indistinguishable from their Schwarzschild values, we propose a simple metric which depends on three independent parameters (coefficients of the parametrization). Variation of these three parameters can, nevertheless, lead to the two distinctive features. The first is the black-hole temperature, and consequently the Hawking radiation, which can differ a lot from its Schwarzschild limit. The second is the outburst of overtones which become extremely sensitive to small changes of the parameters.

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arXiv2023

Bardeen spacetime as a quantum corrected Schwarzschild black hole: Quasinormal modes and Hawking radiation

The Bardeen black hole holds historical significance as the first model of a regular black hole. Recently, there have been proposed interpretations of the Bardeen spacetime as quantum corrections to the Schwarzschild solution. Our study focuses on investigating the quasinormal modes and Hawking radiation of the Bardeen black hole. We have observed that previous studies on the quasinormal modes for the Bardeen black hole suffer from inaccuracies that cannot be neglected. Therefore, we propose accurate calculations of the quasinormal modes for scalar, electromagnetic, and neutrino fields in the Bardeen spacetime. Additionally, we have computed the grey-body factors and analyzed the emission rates of Hawking radiation. Even when the quantum correction is small and the fundamental mode only slightly differs from its Schwarzschild value, the first several overtones deviate at an increasingly stronger rate. This deviation leads to the appearance of overtones with very small real oscillation frequencies. This outburst of overtones is closely linked to the fact that the quantum-corrected black hole differs from its classical limit primarily near the event horizon. Moreover, the intensity of the Hawking radiation is significantly suppressed (up to three orders of magnitude) by the quantum correction.

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arXiv2023

Non-Schwarzschild black-hole metric in four dimensional higher derivative gravity: analytical approximation

Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. Lü, A. Perkins, C. Pope, K. Stelle [Phys.Rev.Lett. 114 (2015), 171601] found a numerical solution describing a spherically symmetric non-Schwarzschild asymptotically flat black hole in the Einstein gravity with added higher derivative terms. Using the general and quickly convergent parametrization in terms of the continued fractions, we represent this numerical solution in the analytical form, which is accurate not only near the event horizon or far from black hole, but in the whole space. Thereby, the obtained analytical form of the metric allows one to study easily all the further properties of the black hole, such as thermodynamics, Hawking radiation, particle motion, accretion, perturbations, stability, quasinormal spectrum, etc. Thus, the found analytical approximate representation can serve in the same way as an exact solution.

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arXiv2023

Quasinormal modes and grey-body factors of regular black holes with a scalar hair from the Effective Field Theory

The Effective Field Theory (EFT) of perturbations on an arbitrary background geometry with a timelike scalar profile has been recently constructed in the context of scalar-tensor theories. Unlike General Relativity, the regular Hayward metric is realized as an exact background metric in the Effective Field Theory with timelike scalar profile without resorting to special matter field, such as nonlinear electrodynamics. The fundamental quasinormal mode for axial graviational perturbations of this black hole has been considered recently with the help of various methods. Here we make a further step in this direction and find that, unlike the fundamental mode, a few first overtones deviate from their Schwarzschild limit at a much higher rate. This outburst of overtones occurs because the overtones are extremely sensitive to the least change of the near-horizon geometry. The analytical formula for quasinormal modes is obtained in the eikonal regime. In addition, we calculated grey-body factors and showed that the regular Hayward black hole with a scalar hair has a smaller grey-body factor than the Schwarzschild one. Integration of the wave-like equation in the time-domain shows that the power-law tails, following the ring-down phase, are indistinguishable from the Schwarzschild ones at late times.

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arXiv2023

Quasinormal modes of renormalization group improved Dymnikova regular black holes

We find accurate quasinormal frequencies of a quantum corrected black hole constructed in the renormalization group theory via the coordinate-independent iterative procedure, leading to the Dymnikova regular black hole. We show that while the fundamental mode is only slightly affected by the quantum correction, the overtones change at a much stronger rate. This outburst of overtones occurs because of the deformation of the geometry of the Schwarzschild black hole solely near the event horizon. For finding accurate values of overtones we developed a general procedure allowing one to use the Leaver method to metrics which, initially, are not expressed in terms of rational functions.

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arXiv2023

Quasinormal modes in higher derivative gravity: testing the black hole parametrization and sensitivity of overtones

The fundamental quasinormal modes of black holes in higher-derivative gravity given by the Einstein-Weyl action are known to be moderately corrected by the Weyl term. Here we will show that the first several overtones are highly sensitive to even a relatively small Weyl correction, which might be important when representing the earlier stage of the black hole ringdown. In addition, we have solved the problem related to the analytical parametrized approximation of the numerical black hole solution in the Einstein-Weyl theory: In some range of parameters the approximation for the metric developed up to the third order leads to the unusual highly nonmonotonic behavior of the frequencies. We have shown that this problem can be solved via the extension of the parametrization of the metric to higher orders until reaching the regime when the frequencies do not change with further increasing of the order.

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arXiv2023

Bernstein spectral method for quasinormal modes of a generic black hole spacetime and application to instability of dilaton-de Sitter solution

We present the improved Mathematica code which computes quasinormal frequencies with the help of the Bernstein spectral method for a general class of black holes, allowing for asymptotically flat, de Sitter or anti-de Sitter asymptotic. The method is especially efficient when searching for purely imaginary and unstable modes and here it is used for detecting the instability region of a charged scalar field in the background of the charged asymptotically de Sitter dilatonic black hole. We show that the instability has superradiant nature and the dilaton field essentially influences the region of instability.

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arXiv2022

Nonoscillatory gravitational quasinormal modes and telling tails for Schwarzschild-de Sitter black holes

We show that the quasinormal spectrum of gravitational perturbations of Schwarzschild - de Sitter black holes contains a new branch of purely imaginary modes. These modes are not algebraically special and we showed that the sum of them form the well-known in the literature exponential asymptotic tail. When the ratio of the event horizon radius to the cosmological horizon vanishes, these quasinormal modes approach modes of empty de Sitter spacetime. Thus, the spectrum consists of the two branches: Schwarzschild branch deformed by the cosmological constant and de Sitter branch deformed by the black hole mass. While the de Sitter branch contains purely imaginary modes only, the oscillatory modes (with nonzero real part) of the Schwarzschild branch can also become purely imaginary for some values of the cosmological constant, for which they approach the algebraically special mode.

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arXiv2022

How general is the strong cosmic censorship bound for quasinormal modes?

Hod's proposal claims that the least damped quasinormal mode of a black hole must have the imaginary part smaller than half of the surface gravity at the event horizon. The Strong Cosmic Censorship in General Relativity implies that this bound must be even weaker: half of the surface gravity at the Cauchy horizon. The appealing question is whether these bounds are limited by the Einstein theory only? Here we will present numerical evidence that once the black hole size is much smaller than then the radius of the cosmological horizon, both the Hod's proposal and the strong cosmic censorship bound for quasinormal modes are satisfied for general spherically symmetric black holes in an arbitrary metric theory of gravity. The low-lying quasinormal frequencies have the universal behavior in this regime and do not depend on the near-horizon geometry, but only on the asymptotic parameters: the value of the cosmological constant and black hole mass.

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arXiv2022

Quasinormal ringing of regular black holes in asymptotically safe gravity: the importance of overtones

Asymptotically safe gravity is based on the idea that the main contribution to the Schwarzschild-like black hole spacetime is due to the value of the gravitational coupling which depends on the distance from the origin and approaches its classical value in the far zone. However, at some stage this approach has an arbitrariness of choice of some identification parameter. The two cases of identification are considered here: first, by the modified proper length (the Bonanno-Reuter metric), and second, by the Kretschmann scalar (the metric for this case coincides, up to the redefinition of constants, with the Hayward metric). Even though the quasinormal modes of these metrics have been extensively studied, a number of interesting points were missed. We have found that quasinormal modes are qualitatively similar for both types of identification. The deviation of the fundamental mode from its Schwarzschild limit may be a few times larger than it was claimed in the previous studies. The striking deviation from the Schwarzschild limit occurs for overtones, being as large as hundreds of percent even when the fundamental mode is almost coinciding with the Schwarzschild one. This happens because the above metrics are very close to the Schwarzschild one everywhere, except a small region near the event horizon, which is crucial for overtones. The spectrum of both metrics contains purely imaginary (non-oscillatory) modes, which, for some values of parameters, can appear already at the second overtone.

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arXiv2022

Further clarification on quasinormal modes/circular null geodesics correspondence

The well-known duality between quasinormal modes of any stationary, spherically symmetric and asymptotically flat or de Sitter black hole and parameters of the circular null geodesic was initially claimed for gravitational and test field perturbations. According to this duality the real and imaginary parts of the $\ell \gg n$ quasinormal mode (where $\ell$ and $n$ are multipole and overtone numbers respectively) are multiples of the frequency and instability timescale of the circular null geodesics respectively. Later it was shown that the duality is guaranteed only for test fields and may be broken for gravitational and other non-minimally coupled fields. Here, we farther specify the duality and prove that even when the duality is guaranteed it may not represent the full spectrum of the $\ell \gg n$ modes, missing the quasinormal frequencies which cannot be found by the standard WKB method. In particular we show that this always happens for an arbitrary asymptotically de Sitter black holes and further argue that, in general, this might be related to sensitivity of the quasinormal spectrum to geometry deformations near the boundaries.

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arXiv2022

Solutions of the Einstein equations for a black hole surrounded by a galactic halo

Various profiles of matter distribution in galactic halos (such as Navarro-Frenk-White, Burkert, Hernquist, Moore, Taylor-Silk and others) are considered here as the source term for the Einstein equations. We solve these equations and find exact solutions which represent the metric of a central black hole immersed in a galactic halo. Even though in the general case the solution is numerical, very accurate general analytical metric, which includes all the particular models, are found in the astrophysically relevant regime, when the mass of the galaxy is much smaller than the characteristic scale in the halo.

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arXiv2022

Quasinormal ringing of general spherically symmetric parametrized black holes

The general parametrization of spherically symmetric and asymptotically flat black-hole spacetimes in arbitrary metric theories of gravity was suggested in [3]. The parametrization is based on the continued fraction expansion in terms of the compact radial coordinate and has superior convergence and strict hierarchy of parameters. It is known that some observable quantities, related to particle motion around the black hole, such as the eikonal quasinormal modes, radius of the shadow, frequency at the innermost stable circular orbit, and others, depend mostly on only a few of the lowest coefficients of the parametrization. Here we continue this approach by studying the dominant (low-lying) quasinormal modes for such generally parametrized black holes. We show that, due to the hierarchy of parameters, the dominant quasinormal frequencies are also well determined by only the first few coefficients of the expansion for the so-called moderate black-hole geometries. The latter are characterized by a relatively slow change of the metric functions in the radiation zone near the black hole. The nonmoderate metrics, which change strongly between the event horizon and the innermost stable circular orbit are usually characterized by echoes or by the distinctive (from the Einstein case) quasinormal ringing which does not match the current observational data. Therefore, the compact description of a black-hole spacetime in terms of the truncated general parametrization is an effective formalism for testing strong gravity and imposing constraints on allowed black-hole geometries.

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arXiv2022

Analytic formula for quasinormal modes in the near-extreme Kerr-Newman-de Sitter spacetime governed by a non-Pöschl-Teller potential

Quasinormal modes of scalar, electromagnetic, and gravitational fields in the extreme Schwarzschild-de Sitter background are known to be expressed in analytic form as eigenvalues of the Pöschl-Teller wavelike equation. We show that perturbations of fermionic fields (given by Dirac and Rarita-Schwinger equations) do not lead to the Pöschl-Teller effective potential. Nevertheless, using the Frobenius method we find quasinormal modes analytically in this case as well. We write down the analytical formula for quasinormal frequencies of the near-extreme Schwarzschild-de Sitter black holes, which is valid for both bosonic and fermionic fields. We further extend the analysis to the case of charged rotating black holes and find a general analytical formula for quasinormal modes of the fields of various spin for the near extreme Kerr-Newman-de Sitter spacetime.

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