arXiv subjects

R. A. Konoplya

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

At least 19 recordsLinked to original sources

arXiv2026

WKB approximation for quasi-bound states and trapped modes

We develop a largely automatic semi-analytic method for calculating weakly damped quasi-bound states and trapped modes supported by a local minimum of an effective potential. The real part of the frequency is obtained from an arbitrarily high-order local WKB expansion and Padé resummation, while the exponentially small imaginary part is estimated using the Gamow approximation for tunnelling through one or two potential barriers. Because the local quantization requires only derivatives of the potential at its minimum, the method applies readily to non-rational effective potentials and to different compact-object geometries. We provide a Mathematica notebook implementing the procedure. Comparisons with continued-fraction and direct numerical results for massive scalar fields around Schwarzschild and Kerr black holes and for axial trapped modes of a uniform-density star show that the method yields accurate real frequencies and useful estimates of decay rates outside the superradiant regime.

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arXiv2026

Quasinormal modes of four-dimensional regular black holes in quasi-topological gravity: Overtones' outburst via WKB method

We study quasinormal modes of scalar, electromagnetic, and Dirac perturbations of four-dimensional regular black holes arising in non-polynomial quasi-topological gravity. Starting from a more general class of metric functions constructed within the same framework, from which two representative cases are selected for detailed analysis, we examine their spectral properties. While the fundamental mode changes smoothly with the regularization parameter, higher overtones display a markedly enhanced sensitivity to near-horizon modifications, leading to the characteristic outburst of overtones. Remarkably, pushing the WKB approximation to sufficiently high orders with Pade resummation already allows one to detect the onset of this effect. Time-domain analysis and the Leaver method confirm that the relative error of the higher-order WKB approach is much smaller than the observed effect. Our results indicate that overtone dynamics provides a sensitive probe of geometrically regular black holes and that high-order WKB methods remain capable of capturing nontrivial spectral features beyond the fundamental mode.

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arXiv2026

Dark matter halo as a source of regular black-hole geometries

We construct exact black hole solutions free of curvature singularities, sourced by dark matter halos described by galactic density profiles. Regularity of the geometry is ensured by adopting the relation $P_{r}=-ρ$ between radial pressure and density, which is consistent with the phenomenological freedom of halo models. Under the assumptions of regularity and the weak-energy condition, sufficiently dense dark matter halos can give rise to asymptotically flat, singularity-free black holes embedded in a galactic environment. These regular black holes are shown to be stable under axial perturbations. In particular, we obtain solutions corresponding to Einasto and Dehnen-type dark matter profiles. We further compute the shadow radii and Lyapunov exponents associated with photon circular orbits around these black holes.

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arXiv2025

Primary hairs may create echoes

In most scenarios studied so far, the appearance of echoes in the ringdown signal requires modifications external to the black hole itself, such as the presence of matter in the near-horizon region, quantum field clouds, or exotic compact objects like wormholes that effectively introduce additional peaks in the effective potential. In this work we show that echoes can naturally arise in a different setting: black holes endowed with primary Proca-Gauss-Bonnet hair. We demonstrate that the primary hair modifies the effective potential in such a way that a second peak is formed, giving rise to late-time echoes without invoking any external environment or exotic horizon-scale physics. Using both the higher-order WKB method with Padé resummation and time-domain integration, we compute the quasinormal spectrum for scalar and Dirac test fields and show the appearance of these echoes. Our results highlight a novel mechanism by which primary hairs alone can leave observable imprints on the ringdown signal of black holes in modified gravity.

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arXiv2025

Primary Proca Hair and the Double-Peak Optics of Black Holes

We study the optical properties of black holes endowed with primary Proca hair, focusing on the distinctive double-peak structure generated in the effective potential by the massive vector field. This novel feature drastically modifies the geodesic motion of both photons and massive particles, leading to qualitatively new dynamical and observational signatures. We derive and analyze the effective potentials, classify time-like and null geodesics, and identify the conditions for multiple circular orbits. Particular attention is devoted to the photon sphere structure, the associated shadows, and lensing phenomena. Our analysis reveals that, for a broad range of parameters, the black-hole shadow can acquire a two-boundary structure and exhibit additional inner rings, unlike the standard Schwarzschild case. These modifications provide potentially observable imprints of Proca hair in electromagnetic spectra, highlighting the relevance of double-barrier optical phenomena for current and future observations of strong-gravity environments.

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arXiv2025

Massive fields affected by echoes: New physics vs. astrophysical environment

Unlike the perturbations of massless fields, the asymptotic tails of massive fields exhibit oscillations and decay slowly, following a power-law envelope. In this work, considering various scenarios admitting (either fundamental or effective) massive scalar and gravitational fields, we demonstrate that bump deformations in the effective potential, either in the near-horizon or far-field regions, modify these asymptotic oscillatory tails. Specifically, the power-law envelope transitions to a more complex oscillatory pattern, which cannot be easily fitted to a simple formula. This behavior is qualitatively different from the echoes of massless fields, which appear mainly during the quasinormal ringing stage and are considerably suppressed at the asymptotic tails. We show that in some models echoes may considerably amplify the signal at the stage of asymptotic tails.

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arXiv2025

Charged black hole surrounded by a galactic halo in de Sitter universe

Assuming a sufficiently general form for the matter distribution function of a galactic halo, we have derived solutions to the Einstein-Maxwell equations describing a charged black hole embedded in such a halo, while also allowing for a non-zero cosmological constant. These solutions generalize our earlier results for neutral black holes in asymptotically flat spacetime. As specific realizations of the general distribution, we consider the Hernquist, Navarro-Frenk-White, Burkert, Taylor-Silk, and Moore halo profiles, thereby capturing a broad range of astrophysically motivated scenarios.

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arXiv2025

Transition from Regular Black Holes to Wormholes in Covariant Effective Quantum Gravity: Scattering, Quasinormal Modes, and Hawking Radiation

Utilizing the Hamiltonian constraints approach, a quantum-corrected solution has been derived \cite{Zhang:2024ney}, which describes either a regular black hole or a traversable wormhole, contingent upon the value of the quantum parameter. In this work, we compute the quasinormal modes associated with axial gravitational and test fields' perturbations of these objects. We see that due to quantum corrections near the event horizon, the first several overtones deviate from their Schwarzschild values at an increasing rate. The transition between the black hole and wormhole states is marked by modifications in the late-time signal. Our findings reveal that the fundamental quasinormal modes of quantum-corrected black holes exhibit only slight deviations from those of the classical Schwarzschild solution. However, at the transition, the spectrum undergoes significant changes, with the wormhole state characterized by exceptionally long-lived quasinormal modes. In addition, we calculate absorption cross-sections of partial waves, grey-body factors and energy emission rates of Hawking radiation.

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arXiv2025

Overtones' outburst and Hawking evaporation of Kazakov-Solodukhin quantum corrected black hole

The Kazakov-Solodukhin black hole metric represents a spherically symmetric deformation of the Schwarzschild solution due to quantum-gravity corrections. Assuming the absence of nonspherical deformations of the metric, this problem was solved nonperturbatively. In this study, we investigate the intensity of Hawking radiation in the background of such quantum-corrected black holes and the behavior of their quasinormal modes (QNM). Our findings indicate that while the geometry and such classical characteristics as the fundamental QNM frequencies or the shadow radius are only slightly altered, the Hawking radiation and the frequencies of QNM overtones of sufficiently small black holes change much more significantly. This Hawking radiation enhancement arises due to much larger grey-body factors, while the Hawking temperature remains unaffected. The effect becomes significant at the latest stage of black hole evaporation.

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arXiv2025

Correspondence between grey-body factors and quasinormal frequencies for rotating black holes

Although the proper oscillation frequencies of black holes (quasinormal modes) and the grey-body factors, which determine the scattering properties of black holes, represent two distinct spectral problems with different boundary conditions, a recent study has revealed an intrinsic connection between these quantities. We have shown that the correspondence between grey-body factors and quasinormal modes, previously established for spherically symmetric and asymptotically flat black holes, also extends to general parametrized axially symmetric black holes. This correspondence is limited to non-superradiant waves.

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arXiv2025

Hawking radiation of renormalization group improved regular black holes

We consider a renormalization group approach based on the idea that the primary contribution to the Schwarzschild-like black hole spacetime arises from the value of the gravitational coupling. The latter depends on the distance from the origin and approaches its classical value in the far zone. However, at some stage, this approach introduces an arbitrariness in choosing an identification parameter. There are three approaches to the identification: the modified proper length (the Bonanno-Reuter metric), the Kretschmann scalar (the Hayward metric), and an iterative, and, in a sense, coordinate-independent procedure (Dymnikova solution). Using the WKB method, we calculated grey-body factors for the Standard Model massless test fields and their corresponding energy emission rates. For all of these solutions, we found that the intensity of Hawking radiation of massless fields is significantly suppressed by several or more orders once the quantum correction is taken into consideration. This indicates that the effect of suppression of the Hawking radiation may be appropriate to the quantum corrected black holes in asymptotically safe gravity in general and is independent on the particular choice of the identification parameter.

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arXiv2024

Probing the Effective Quantum Gravity via Quasinormal Modes and Shadows of Black Holes

Two quantum-corrected black hole models have recently been proposed within the Hamiltonian constraints approach to quantum gravity, maintaining general covariance \cite{Zhang:2024khj}. We have studied the quasinormal spectra of these black holes using four methods: the higher-order WKB approach with Padé approximants, time-domain integration, Frobenius, and pseudospectral methods. The Frobenius method, in particular, allows us to determine precise values of the frequencies, including the overtones. The two models differ in their choice of quantum parameter $ξ$, and we can distinguish them by their quasinormal spectra. In the first model, increasing the quantum parameter results in higher real oscillation frequencies and damping rates of the fundamental mode. In contrast, the second model shows a decrease in the oscillation frequency of the least-damped mode when the quantum parameter is introduced. We have shown that, while the fundamental mode changes relatively gradually with the quantum parameter, the first few overtones deviate from their Schwarzschild limits at an increasing rate. This results in a qualitatively new behavior: the real parts of the frequencies of the first and higher overtones tend to zero as the quantum parameter increases. In addition to the branch of modes that are perturbative in the quantum parameter, we observe some non-perturbative modes at moderate values of the quantum parameter. Additionally, we have calculated the radii of the shadows cast by these black holes and discussed possible constraints based on observations of Sgt $A^*$. As a byproduct, we tested the method of calculating quasinormal modes of this kind based on a recent agnostic parametrization and showed that while the parametrized formalism could be used for estimating the fundamental mode at small values of the coupling, it is insufficient even for the lowest overtones.

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arXiv2024

Circumventing Quantum Gravity: Black Holes Evaporating into Macroscopic Wormholes

Recently, metrics that describe regular black holes, extreme black holes, or traversable wormholes have been widely discussed. These spacetimes, appearing in scenarios such as the brane world, are contingent on the values of the parameters, with each metric encompassing all three objects. We are considering various known models for these black hole/wormhole interpolating spacetimes and showing that, starting from the macroscopic black holes, all of them must evaporate into macroscopic wormholes, thus avoiding existential problems related to the final stages of black hole evaporation and issues of quantum gravity and black hole remnants. For this purpose, we are calculating the energy emission rates of black holes and the appropriate lifetimes. We argue that some of our conclusions should hold regardless of the specific model, as long as it permits an extremal black hole state with zero temperature at a particular value of the coupling constant.

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arXiv2024

First few overtones probe the event horizon geometry

It is broadly believed that quasinormal modes cannot tell the black-hole near-horizon geometry, because usually the low-lying modes are determined by the scattering of perturbations around the peak of the effective potential. Using the general parametrization of the black-hole spacetimes respecting the generic post-Newtonian asymptotic, we will show that tiny modifications of the Schwarzschild/Kerr geometry in a relatively small region near the event horizon lead to almost the same Schwarzschild/Kerr fundamental mode, but totally different first few overtones. Having in mind that the first several overtones affect the quasinormal ringing at its early and intermediate stage [M. Giesler, M. Isi, M. Scheel, and S. Teukolsky, Phys. Rev. X 9, 041060 (2019)], we argue that the near-horizon geometry could in principle be studied via the first few overtones of the quasinormal spectrum, which is important because corrections to the Einstein theory must modify precisely the near-horizon geometry, keeping the known weak field regime.

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arXiv2024

Correspondence between grey-body factors and quasinormal modes

Quasinormal modes and grey-body factors are spectral characteristics corresponding to different boundary conditions: the former imply purely outgoing waves to the event horizon and infinity, while the latter allow for an incoming wave from the horizon, thus describing a scattering problem. Nevertheless, we show that there is a link between these two characteristics. We establish an approximate correspondence between the quasinormal modes and grey-body factors, which becomes exact in the high-frequency (eikonal) regime. We show that, in the eikonal regime, the grey-body factors of spherically symmetric black holes can be remarkably simply expressed via the fundamental quasinormal mode, while at smaller $\ell$, the correction terms include values of the overtones. This might be interesting in the context of the recently observed connection between grey-body factors and the amplitudes of gravitational waves from black holes. The correspondence might explain why grey-body factors are more stable, i.e. less sensitive, than higher overtones to small deformation of the effective potential.

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arXiv2024

Dymnikova black hole from an infinite tower of higher-curvature corrections

Recently, in [arXiv:2403.04827], it was demonstrated that various regular black hole metrics can be derived within a theory featuring an infinite number of higher curvature corrections to General Relativity. Moreover, truncating this infinite series at the first few orders already yields a reliable approximation of the observable characteristics of such black holes [arXiv:2403.07848]. Here, we further establish the existence of another regular black hole solution, particularly the $D$-dimensional extension of the Dymnikova black hole, within the equations of motion incorporating an infinite tower of higher-curvature corrections. This solution is essentially nonperturbative in the coupling parameter, rendering the action, if it exists, incapable of being approximated by a finite number of powers of the curvature. In addition, we compute the dominant quasinormal frequencies of such black holes using both the Bernstein polynomial method and the 13th order WKB method with Padé approximants, obtaining a high degree of agreement between them.

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arXiv2024

Asymptotic tails of massive gravitons in light of pulsar timing array observations

We demonstrate that the late time oscillatory tails of massive gravitons, present in both massive theories of gravity and effectively in extra-dimensional scenarios, could potentially contribute to gravitational waves with very long wavelengths. However, their impact on recent pulsar timing array observations might be relatively small, predominantly consisting of radiation emitted by black holes in our region of the Milky Way.

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arXiv2024

Infinite tower of higher-curvature corrections: Quasinormal modes and late-time behavior of D-dimensional regular black holes

Recently, Bueno, Cano, and Hennigar [arXiv:2403.04827] proposed a generic approach for incorporating an infinite tower of higher-curvature corrections into the Einstein theory. In this study, we compute quasinormal modes for certain regular D-dimensional black holes resulting from this infinite series of higher-curvature corrections, specifically focusing on the $D$-dimensional extensions of the Bardeen and Hayward black holes. We demonstrate that while the fundamental mode is minimally affected by moderate coupling constants, the higher overtones exhibit significant sensitivity even to small coupling values, yielding unconventional modes characterized by vanishing real oscillation frequencies. When comparing the frequencies derived from the metric truncated at several orders of higher-curvature corrections with those resulting from the infinite series of terms, we observe a rapid convergence of the frequencies to their limit for the complete regular black hole. This validates the extensive research conducted on specific theories with a finite number of higher-curvature corrections, such as the Lovelock theory.

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