On quasinormal modes in 4D black hole solutions in the model with anisotropic fluid

S. V. Bolokhov; V. D. Ivashchuk

doi:10.1140/epjc/s10052-022-10578-5

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2022) 82: 624
https://doi.org/10.1140/epjc/s10052-022-10578-5

Regular Article - Theoretical Physics

On quasinormal modes in 4D black hole solutions in the model with anisotropic fluid

S. V. Bolokhov¹ and V. D. Ivashchuk¹^,2^b

¹ Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198, Moscow, Russian Federation
² Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya St., 119361, Moscow, Russian Federation

^b ivashchuk@mail.ru

Received: 1 February 2022
Accepted: 3 July 2022
Published online: 19 July 2022

Abstract

We consider a family of four-dimensional black hole solutions from Dehnen et al. (Grav Cosmol 9:153 arXiv:gr-qc/0211049, 2003) governed by natural number $q = 1, 2, 3, \dots$ $q= 1, 2, 3 , \dots$ , which appear in the model with anisotropic fluid and the equations of state: $p_{r} = - ρ {(2 q - 1)}^{- 1}$ $p_r = -\rho (2q-1)^{-1}$ , $p_{t} = - p_{r}$ $$p_t = - p_r$$ , where $p_{r}$ $$p_r$$ and $p_{t}$ $$p_t$$ are pressures in radial and transverse directions, respectively, and $ρ > 0$ $\rho > 0$ is the density. These equations of state obey weak, strong and dominant energy conditions. For $q = 1$ $$q = 1$$ the metric of the solution coincides with that of the Reissner–Nordström one. The global structure of solutions is outlined, giving rise to Carter–Penrose diagram of Reissner–Nordström or Schwarzschild types for odd $q = 2 k + 1$ $$q = 2k + 1$$ or even $q = 2 k$ $$q = 2k$$ , respectively. Certain physical parameters corresponding to BH solutions (gravitational mass, PPN parameters, Hawking temperature and entropy) are calculated. We obtain and analyse the quasinormal modes for a test massless scalar field in the eikonal approximation. For limiting case $q = + \infty$ $q = + \infty$ , they coincide with the well-known results for the Schwarzschild solution. We show that the Hod conjecture which connect the Hawking temperature and the damping rate is obeyed for all $q \geq 2$ $q \ge 2$ and all (allowed) values of parameters.

© The Author(s) 2022

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