Schwarzschild black hole and the generalized second law in phantom-dominated universe

TL;DR

This paper investigates the validity of the generalized second law of thermodynamics in a universe dominated by phantom energy containing a Schwarzschild black hole, focusing on transition periods and temperature considerations.

Contribution

It analyzes the conditions under which the generalized second law holds in phantom-dominated universes, including during regime transitions and with different temperature assumptions.

Findings

The law can be satisfied if temperature differs from de Sitter temperature.

The law fails during the transition from quintessence to phantom regime.

Validity depends on the temperature choice and the universe's equation of state.

Abstract

We study the conditions required for validity of the generalized second law in phantom dominated universe in the presence of Schwarzschild black hole. Our study is independent of the origin of the phantom like behavior of the considered universe. We also discuss the generalized second law in the neighborhood of transition (from quintessence to phantom regime) time. We show that even for a constant equation of state parameter the generalized second law may be satisfied provided the temperature is not taken as 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.