Thermodynamics of phantom energy in the presence of a Reissner-Nordstrom black hole

TL;DR

This paper investigates the validity of the generalized second law of thermodynamics in a universe dominated by phantom energy with a Reissner-Nordstrom black hole, considering various conditions including chemical potential and regime transitions.

Contribution

It analyzes the conditions under which the generalized second law holds in phantom energy scenarios with black holes, including effects of chemical potential and regime transitions.

Findings

GSL may be satisfied if temperature is proportional to de Sitter temperature.

GSL does not hold during the transition from quintessence to phantom regime.

GSL holds if phantom energy has a chemical potential and black hole mass exceeds a critical value.

Abstract

In this paper, we study the validity of the generalized second law (GSL) in phantom dominated universe in the presence of a Reissner-Nordstr\"{o}m (RN) black hole. Our study is independent of the origin of the phantom like behavior of the considered universe. We also discuss the GSL in the neighborhood of transition from quintessence to phantom regime. We show that for a constant equation of state parameter, the GSL may be satisfied provided that the temperature is proportional to de Sitter temperature. It is shown that in models with (only) a transition from quintessence to phantom regime the generalized second law does not hold in the transition epoch. Next we show that if the phantom energy has a chemical potential, then the GSL will hold if the mass of black hole is above from a critical value.