arXiv subjects

A. M. Arslanaliev

Publications and source records attributed to A. M. Arslanaliev.

4 recordsLinked to original sources

arXiv2024

Taking the Null-Hypersurface Limit in the Parikh-Wilczek Membrane Approach

We consider subtleties of the horizon (null-hypersurface) limit in the Parikh-Wilczek Membrane Approach to Black Holes. Specifically, we refine the correspondence between the projected Einstein equations of gravity with matter and the Raychaudhuri-Damour-Navier-Stokes (RDNS) equations of relativistic hydrodynamics. For a general configuration of gravity with matter we obtain additional terms in the hydrodynamic equations, which include very specific combinations of the contracted logarithmic derivatives of a parameter (the regularization function) determining the proximity of a stretched membrane to the black hole horizon. Nevertheless, direct computations of the new terms for exact (Schwarzschild and Kerr) black hole solutions prompt the standard form of the RDNS equations, due to the non-expanding horizon property of these solutions. Therefore, the reduction of the extended RDNS equations to their classical form may be viewed as an additional consistency condition in the exact black hole solutions hydrodynamics, and may serve as a non-trivial test for various viable approximations of spacetime metrics. We compare in detail the Parikh-Wilczek Membrane Approach with the Gourgoulhon-Jaramillo method of a null-hypersurface description, as well as give the link of the obtained results to our previous work on the Kerr black holes.

hep-th↗

arXiv2023

Kerr Black Holes within the Membrane Paradigm

We consider the membrane viewpoint a là Parikh-Wilczek on the Kerr solution for a rotating black hole. Computing the stress-energy tensor of a close-to-the-horizon stretched membrane and comparing it to the stress-tensor of a viscous fluid, we recover transport coefficients in terms of the Kerr geometry. Viscosities of the dual fluid remain constant, while the rest of the transport coefficients become complex functions of radial and angle coordinates. We study the qualitative behavior of the pressure, expansion, and energy/momentum densities for two specific black holes: the slowly rotating black hole, with the angular momentum of one percent of the black hole mass squared, and the extremal Kerr black hole. For the Kerr solution in the Boyer-Lindquist coordinates, these transport coefficients generally have poles at different values of the radial coordinate in the range between the horizon and the Schwarzschild radius of the black hole, in dependence on the fixed angle direction. We briefly discuss our findings in the context of a relation between the Membrane Paradigm and the AdS/CFT correspondence, the KSS bound violation, the coordinate choice, and a non-stationary extension of the Kerr solution.

hep-th↗

arXiv2021

Scattering on Quasi-Spherical Black-Holes: Features and Beyond

Recent developments in the gravitational waves interferometry require more pertinent theoretical models of gravitational waves generation and propagation. Untouched possible mechanisms of spin-2 spacetime perturbations production, we will consider their subsequent scattering on other black holes (BHs). Specifically, we consider a generalization of the Regge-Wheeler-Zerilli equations for the case of distorted BHs (BHs surrounded with matter) in Minkowski and Anti-de Sitter spacetimes, the metric potential of which obeys the Liouville equation. We establish significant differences in scattering characteristics of waves of different spins and angular momenta, including the gravitational waves, caused by losing the spherical symmetry of their propagation background. In particular, we demonstrate the strong impact of the background geometry deformation on the grey-body factors, hence on the absorption cross-sections of scattering waves, and explore the issue of stability of the background geometry upon changing the deformation degree parameters.

gr-qc↗

arXiv2017

Dynamics of Bose-Einstein condensate with account of pair correlations

The system of dynamic equations for Bose-Einstein condensate at zero temperature with account of pair correlations is obtained. The spectrum of small oscillations of the condensate in a spatially homogeneous state is explored. It is shown that this spectrum has two branches: the sound wave branch and branch with an energy gap.

cond-mat.stat-mech↗