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

Abstract

Motivated by high interest in Lorentz invariant massive gravity models known as dRGT massive gravity, we present an exact phantom black hole solution in this theory of gravity and discuss the thermodynamic structure of the black hole in the canonical ensemble. Calculating the conserved and thermodynamic quantities, we check the validity of the first law of thermodynamics and the Smarr
relation in the extended phase space. In addition, we investigate both the local and global stability of these black holes and show how massive parameters affect the regions of stability. We extend our study to investigate the optical features of the black holes such as the shadow geometrical shape, energy emission rate, and deflection angle. Also, we discuss how these optical quantities are affected
by massive coefficients. Finally, we consider a massive scalar perturbation minimally coupled to the background geometry of the black hole and examine the quasinormal modes by employing the WKB approximation.

Thermodynamical analysis with extended phase transition of AdS hairy black hole in gravitational decoupling theory

“…The thermodynamical properties of BHs are analyzed by Hawking and Page [76] in asymptotically AdS BHs. The BH stability demands that, we have to investigate the thermal properties at local-level by employing heat capacity and global-level by utilizing the GFE [77,78]. As everyone is aware in the context of canonical ensemble, the BH's local stability can be examined by calculating the heat capacity, while the global stability examined in the grand canonical ensemble by studying the Gibbs free energy (GFE).…”

“…To analyze the heat capacity of the AdS hairy BH, we need to compute its heat capacity to see the effects of the coupling parameter α. The positive (negative) GFE demonstrate that BH globally stable (unstable) [77,80,81] so, we want to study the global stability of AdS hairy BH by using the Gibbs free energy approach. The heat capacity is obtained as…”

Hawking–Page transition and the dual relations of anti-de Sitter black holes surrounded by dark energy in general dimensions

“…In this paper, we will focus on the effect of dark energy on the Hawking-Page transition and the dual relation equation (1), including phantom dark energy and quintessence dark energy. Recently, black holes surrounded by phantom dark energy and quintessence dark energy and their thermodynamics have attracted considerable interest (see references [12,21,[38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53] and [30,[54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71], respectively). Black holes surrounded by dark energy could be used as a theoretical laboratory for studying black hole physics and investigating the theoretical properties and implications of phantom dark energy and quintessence dark energy.…”