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
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
Received:
1
February
2022
Accepted:
3
July
2022
Published online:
19
July
2022
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 
, which appear in the model with anisotropic fluid and the equations of state: 
, 
, where 
and 
are pressures in radial and transverse directions, respectively, and 
is the density. These equations of state obey weak, strong and dominant energy conditions. For 
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 
or even 
, 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 
, 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 
and all (allowed) values of parameters.
© The Author(s) 2022
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