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

TL;DR

This paper investigates quasinormal modes of a family of 4D black hole solutions influenced by anisotropic fluid, revealing their properties, global structure, and how they conform to the Hod conjecture across different parameters.

Contribution

It introduces a new family of black hole solutions with anisotropic fluid and analyzes their quasinormal modes, global structure, and thermodynamic properties, extending known results to a broader class.

Findings

Quasinormal modes match Schwarzschild results as q approaches infinity.

Hod conjecture holds for all q ≥ 2 and allowed parameters.

Global structure varies with q, resembling Reissner-Nordström or Schwarzschild types.

Abstract

We consider a family of 4-dimensional black hole solutions from Dehnen et al. ( Grav. Cosmol. 9:153, arXiv: gr-qc/0211049, 2003) governed by natural number $q= 1, 2, 3 , \dots$, which appear in the model with anisotropic fluid and the equations of state: $p_r = -\rho (2q-1)^{-1}$, $p_t = - p_r$, where $p_r$ and $p_t$ are pressures in radial and transverse directions, respectively, and $\rho > 0$ is the density. These equations of state obey weak, strong and dominant energy conditions. For $q = 1$ the metric of the solution coincides with that of the Reissner-Nordstr\"om one. The global structure of solutions is outlined, giving rise to Carter-Penrose diagram of Reissner-Nordstr\"om or Schwarzschild types for odd $q = 2k + 1$ or even $q = 2k$, 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 $q = + \infty$, 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 $q \geq 2$ and all (allowed) values of parameters.