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

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-Nordström one. The global structure of solutions is outlined, giving rise to Carter-Penrose diagram of Reissner-Nordström 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 $q\ge 2$ and all (allowed) values of parameters.

20 pages, 6 figures, LaTex. Two Remarks are added, a paragraph in subsection 4.1 is deleted, several typos are eliminated

References in corpus (5)

• Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations
• Are eikonal quasinormal modes linked to the unstable circular null geodesics?
• Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing
• Quasinormal modes of Dirac field in the Einstein-dilaton-Gauss-Bonnet and Einstein-Weyl gravities
• Quasinormal modes in the field of a dyon-like dilatonic black hole

Cited by in corpus (5)

• Analytic expressions for quasinormal modes and grey-body factors in the eikonal limit and beyond
• Long-lived quasinormal modes, grey-body factors and absorption cross-section of the black hole immersed in the Hernquist galactic halo
• Gravitational Spectra and Wave Propagation in Regular Black Holes Supported by a Dehnen Halo
• Long-lived modes and grey-body factors of massive fields in quantum-corrected (Hayward) black holes
• Photon spheres near black holes in a model with anisotropic fluid