Thermodynamics of EiBI-AdS black holes with global monopole

TL;DR

This paper explores the thermodynamics and phase transitions of EiBI-AdS black holes with global monopoles, applying the Euclidean action formalism to reveal conditions for different phase behaviors and confirming the first law and Smarr's law.

Contribution

It is the first study to analyze the thermodynamics of EiBI-AdS black holes with global monopoles using the full Euclidean action formalism and to identify the forbidden parameter ranges.

Findings

Confirmed the first law of black hole mechanics for these solutions.

Identified the forbidden parameter range for the EiBI-AdS black holes with monopoles.

Discovered phase transition behaviors analogous to Schwarzschild AdS and flat spacetimes.

Abstract

It is well-known that black hole can be endowed with topological charge coming as a result of phase transition(s) in the early universe. It has also recently been revealed that such object might exist in one of the modified theory of gravity called the Eddington-inspired-Born-Infeld (EiBI) theory. Here we shall investigate the the possibility of phase transitions, and in general thermodynamic phenomena, of EiBI-anti-de Sitter (AdS) black hole with (topologically-charged) global monopole. This is the first work that applies the full Euclidean action formalism in this model. We provide a counterterm to cancel inifinities and argue that it is the most suitable among other possibilities. Our investigation reveals that the state variables obtained are found to obey the first law of the black hole mechanics and the Smarr's law for black holes with $\Lambda\neq0$. Related to the second feature, we obtained the forbidden range of parameter space for EiBI AdS black hole with global monopole, which corresponds to $\frac{-(1 - \Delta)}{\Lambda } \leq \kappa \leq -\frac{1}{\Lambda }$. The dependencies on $\Lambda$, the EiBI constant $\kappa$ and the global monopole charge $\eta$ of the state variables and state functions obtained manifests in a Schwarzchild AdS-like phase transition for black holes with parameters below the lower bound of the forbidden range, and could also manifest in a Schwarzschild-flat like phase behavior for black holes with parameters above the higher bound of the forbidden range.