Three-dimensional AdS black holes in massive-power-Maxwell theory

Abstract

Recently, it was shown that power-Maxwell (PM) theory can remove the singularity of electric field [1]. Motivated by great interest in three-dimensional black holes and a surge of success in studying massive gravity from both the cosmological and astrophysical point of view, we investigate such black hole solutions in de Rham, Gabadadze and Tolley (dRGT) massive theory of gravity in the presence of PM electrodynamics. First, we extract exact three-dimensional solutions in the PM-dRGT massive gravity. Then we study geometrical properties including type of singularity and asymptotic behavior, and show that although there is a singularity at the origin for asymptotical (A)dS, only AdS solutions are covered by an event horizon. Calculating conserved and thermodynamic quantities, we check the validity of the first law of thermodynamics for the corresponding solutions and examine the stability of these black holes in context of canonical ensemble. We continue with the calculation of the optical features of this kind of black holes such as the shadow geometrical shape, the energy emission rate and the deflection angle. Taking into account these optical quantities, we analysis the effective role of the parameters of models on them. We also employ the correspondence between the quasinormal modes in the eikonal limit and shadow radius to study the scalar field perturbations in these backgrounds. Finally, we take advantage of the WKB method and investigate how the quasinormal modes will be disturbed for massive particles.

Orbits of light rays in (1＋2)-dimensional Einstein–power–Maxwell gravity: Exact analytical solution to the null geodesic equations

“…This is to be contrasted to what happens in the case of the standard Reissner-Nordström solution [48]. Finally, a toy model that generalizes Maxwell's theory in a straightforward manner leads to the so called Einstein-power-Maxwell (EpM) theory [49][50][51][52][53][54][55][56][57][58][59][60][61][62], described by a Lagrangian density of the form L(F ) ∼ F k , where F is the Maxwell invariant, and k is an arbitrary rational number. One of the advantages of EpM theory is that the nice conformal properties of the four-dimensional Maxwell's theory are preserved in any number of space-time dimensionality D, provided that the power k is chosen to be k = D/4, as it is easy to verify that for this particular value the electromagnetic stress-energy tensor becomes traceless.…”

Thermodynamics and optical properties of phantom AdS black holes in massive gravity

“…By considering this theory of massive gravity, many works were done. For example, black hole solutions and their thermodynamic properties are investigated in [31][32][33][34][35][36][37][38][39][40]. It was shown that there is a correspondence between black hole solutions of conformal and this theory of massive gravity [41].…”