arXiv subjects

A. Zhidenko

Publications and source records attributed to A. Zhidenko.

84 records · Page 5Linked to original sources

arXiv2008

Stability of higher dimensional Reissner-Nordstrom-anti-de Sitter black holes

We investigate stability of the D-dimensional Reissner-Nordstrom-anti-de-Sitter metrics as solutions of the Einstein-Maxwell equations. We have shown that asymptotically anti-de Sitter black holes are dynamically stable for all values of charge and anti-de Sitter radius in $D=5,6...11$ dimensional space-times. This does not contradict to dynamical instability of RN-AdS black holes found by Gubser in $\mathcal{N}=8$ gauged supergravity, because the latter instability comes from the tachyon mode of the scalar field, coupled to the system. Asymptotically AdS black holes are known to be thermodynamically unstable for some region of parameters, yet, as we have shown here, they are stable against gravitational perturbations.

hep-th↗

arXiv2008

Looking at the Gregory-Laflamme instability through quasi-normal modes

We study evolution of gravitational perturbations of black strings. It is well known that for all wavenumber less than some threshold value, the black string is unstable against scalar type of gravitational perturbations, which is named the Gregory-Laflamme instability. Using numerical methods, we find the quasinormal modes and time-domain profiles of the black string perturbations in the stable sector and also show the appearance of the Gregory-Laflamme instability in the time domain. The dependence of the black string quasinormal spectrum and late time tails on such parameters as the wave vector and the number of extra dimensions is discussed. There is a numerical evidence that in the threshold point of instability the static solution of the wave equation is dominant. For wavenumbers slightly larger than the threshold value, in the region of stability, we see tiny oscillations with very small damping rate. While, for wavenumbers slightly smaller than the threshold value, in the region of the Gregory-Laflamme instability, we observe tiny oscillations with very small growth rate. We also find the level crossing of imaginary part of quasinormal modes between the fundamental mode and the first overtone mode, which accounts for the peculiar time domain profiles.

hep-th↗

arXiv2008

(In)stability of D-dimensional black holes in Gauss-Bonnet theory

We make an extensive study of evolution of gravitational perturbations of D-dimensional black holes in Gauss-Bonnet theory. There is an instability at higher multi-poles $\ell$ and large Gauss-Bonnet coupling $α$ for $D= 5, 6$, which is stabilized at higher $D$. Although small negative gap of the effective potential for scalar type of gravitational perturbations, exists for higher $D$ and whatever $α$, it does not lead to any instability.

hep-th↗

arXiv2007

Perturbations of Schwarzschild black holes in laboratories

It is well-known that the perturbations of Schwarzschild black holes are governed by a wave equation with some effective potential. We consider perturbations of a gas in a tube called Laval nozzle, which is narrow in the middle and has a sonic point in the throat. By equating the wave equation in a Laval nozzle of an arbitrary form with the wave equation of spin-s perturbations of Schwarzschild black holes, we find the exact expression for the form of the Laval nozzle, for which acoustic perturbations of the gas flow corresponds to the general form of perturbations of Schwarzschild black holes. This allows observation, in a laboratory, of the acoustic waves, which are analogue of damping quasinormal oscillations of Schwarzschild black holes. The found exact acoustic analog allows to observe also some other phenomena governed by the wave equation, such as the wave scattering and tunneling.

hep-th↗

arXiv2007

Stability of multidimensional black holes: complete numerical analysis

We analyze evolution of gravitational perturbations of D-dimensional Schwarzschild, Reissner-Nordström, and Reissner-Nordstrom-de Sitter black holes. It is known that the effective potential for the scalar type of gravitational perturbations has negative gap near the event horizon. This gap, for some values of the parameters Q (charge), Lambda (cosmological constant) and D (number of space-time dimensions), cannot be removed by S-deformations. Thereby, there is no proof of (in)stability for those cases. In the present paper, by an extensive search of quasinormal modes, both in time and frequency domains, we shall show that spherically symmetric static black holes with arbitrary charge and positive (de Sitter) lambda-term are stable for D=5, 6, >...11. In addition, we give a complete numerical data for all three types (scalar, vector and tensor) of gravitational perturbations for multi-dimensional black holes with charge and Lambda-term. The influence of charge, Lambda-term and number of extra dimensions on black hole quasinormal spectrum is discussed.

hep-th↗

arXiv2007

Late time tails of the massive vector field in a black hole background

We investigate the late-time behavior of the massive vector field in the background of the Schwarzschild and Schwarzschild-de Sitter black holes. For Schwarzschild black hole, at intermediately late times the massive vector field is represented by three functions with different decay law $Ψ_{0} \sim t^{-(\ell + 3/2)} \sin{m t}$, $Ψ_{1} \sim t^{-(\ell + 5/2)} \sin{m t}$, $Ψ_{2} \sim t^{-(\ell + 1/2)} \sin{m t}$, while at asymptotically late times the decay law $Ψ\sim t^{-5/6} \sin{(m t)}$ is universal, and does not depend on the multipole number $\ell$. Together with previous study of massive scalar and Dirac fields where the same asymptotically late-time decay law was found, it means, that the asymptotically late-time decay law $\sim t^{-5/6} \sin{(m t)}$ \emph{does not depend} also \emph{on the spin} of the field under consideration. For Schwarzschild-de Sitter black holes it is observed two different regimes in the late-time decay of perturbations: non-oscillatory exponential damping for small values of $m$ and oscillatory quasinormal mode decay for high enough $m$. Numerical and analytical results are found for these quasinormal frequencies.

gr-qc↗

arXiv2007

Gravitational spectrum of black holes in the Einstein-Aether theory

Evolution of gravitational perturbations, both in time and frequency domains, is considered for a spherically symmetric black hole in the non-reduced Einstein-Aether theory. It is shown that real oscillation frequency and damping rate are larger for the Einstein-Aether black hole than for the Schwarzschild black hole. This may provide an opportunity to observe aether in the forthcoming experiments with new generation of gravitational antennas.

hep-th↗

arXiv2006

Perturbations and quasi-normal modes of black holes in Einstein-Aether theory

We develop a new method for calculation of quasi-normal modes of black holes, when the effective potential, which governs black hole perturbations, is known only numerically in some region near the black hole. This method can be applied to perturbations of a wide class of numerical black hole solutions. We apply it to the black holes in the Einstein-Aether theory, a theory where general relativity is coupled to a unit time-like vector field, in order to observe local Lorentz symmetry violation. We found that in the non-reduced Einstein-Aether theory, real oscillation frequency and damping rate of quasi-normal modes are larger than those of Schwarzschild black holes in the Einstein theory.

gr-qc↗

arXiv2006

Quasi-Normal Modes of Brane-Localised Standard Model Fields II: Kerr Black Holes

This paper presents a comprehensive study of the fundamental quasinormal modes of all Standard Model fields propagating on a brane embedded in a higher-dimensional rotating black hole spacetime. The equations of motion for fields with spin $s=0, 1/2$ and 1 propagating in the induced-on-the-brane background are solved numerically, and the dependence of their QN spectra on the black hole angular momentum and dimensionality of spacetime is investigated. It is found that the brane-localised field perturbations are longer-lived when the higher-dimensional black hole rotates faster, while an increase in the number of transverse-to-the-brane dimensions reduces their lifetime. Finally, the quality factor $Q$, that determines the best oscillator among the different field perturbations, is investigated and found to depend on properties of both the particular field studied (spin, multipole numbers) and the gravitational background (dimensionality, black hole angular momentum number).

gr-qc↗

arXiv2006

Stability and quasinormal modes of the massive scalar field around Kerr black holes

We find quasinormal spectrum of the massive scalar field in the background of the Kerr black holes. We show that all found modes are damped under the quasinormal modes boundary conditions when $μM$ is not large, thereby implying stability of the massive scalar field. This complements the region of stability determined by the Beyer inequality for large masses of the field. We show that, similar to the case of a non-rotating black holes, the massive term of the scalar field does not contribute in the regime of high damping. Thereby, the high damping asymptotic should be the same as for the massless scalar field.

gr-qc↗

arXiv2005

High overtones of Dirac perturbations of a Schwarzschild black hole

Using the Frobenius method, we find high overtones of the Dirac quasinormal spectrum for the Schwarzschild black hole. At high overtones, the spacing for imaginary part of $ω_{n}$ is equidistant and equals to $\Im{ω_{n+1}}-\Im{ω_{n}} =i/8M$, ($M$ is the black hole mass), which is twice less than that for fields of integer spin. At high overtones, the real part of $ω_{n}$ goes to zero. This supports the suggestion that the expected correspondence between quasinormal modes and Barbero-Immirzi parameter in Loop Quantum Gravity is just a numerical coincidence.

hep-th↗

arXiv2004

High overtones of Schwarzschild-de-Sitter quasinormal spectrum

We find the high overtones of gravitational and electromagnetic quasinormal spectrum of the Schwarzschild-de Sitter black hole. The calculations show that the real parts of the electromagnetic modes asymptotically approach zero. The gravitational modes show more peculiar behavior at large $n$: the real part oscillates as a function of imaginary even for very high overtones and these oscillations settles to some "profile" which just repeats itself with further increasing of the overtone number $n$. This lets us judge that $Re ω$ is not a constant as $n \to \infty$ but rather some oscillating function. The spacing for imaginary part $ Im ω_{n+1}-Im ω_{n}$ for both gravitational and electromagnetic perturbations at high $n$ oscillates as a function of $n$ around the value $k_{e}$, where $k_{e}$ is the surface gravity. In addition we find the lower QN modes for which the values obtained with numerical methods are in a very good agreement with those obtained through the 6th order WKB technique.

hep-th↗