Photon spheres near black holes in a model with anisotropic fluid

Abstract

The semi-review paper studies the null geodesics which appear for black hole solutions in the gravitational $4d$ model with anisotropic fluid. The equations of state for the fluid and solutions itselves depend upon integer parameter $q=1,2,...$: $p_r=-\rho c^2(2q-1{)}^{-1},p_t=-p_r$, where $\rho$ is the mass density, $c$ is speed of light, $p_r$ and $p_t$ are pressures in radial and transverse to radial directions, respectively. The circular null geodesics are explored and the master equation for radius $r_{\ast }$ of photon sphere is outlined as well as the proposition on existence and uniqueness of the solution to master equation obeying $r_{\ast }>r_h$, where $r_h$ is horizon radius. The relations for spectrum of quasinormal modes for a test massless scalar field in the eikonal approximation are overviewed and compared with cyclic frequencies of circular null geodesics. The shadow angles are explored.

arXiv comment10 pages, LaTex, 1 figure

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Cited by in corpus (1)

• Photon Sphere for a Dilatonic Dyonic Black Hole in a Model with an Abelian Gauge Field and a Scalar Field