Black Hole Thermodynamics with Dynamical Lambda

TL;DR

This paper investigates the thermodynamics of black holes during a slow-roll transition between different de Sitter phases, analyzing horizon area changes and the extended first law in a scalar field model with dynamical cosmological constant.

Contribution

It introduces a detailed analysis of black hole thermodynamics with a dynamical cosmological constant during cosmological phase transitions.

Findings

Late time de Sitter phase has finite cosmological tension with underdamped scalar oscillations.

Fractional change in horizon area correlates with change in effective cosmological constant.

Extended first law of thermodynamics holds during the transition.

Abstract

We study evolution and thermodynamics of a slow-roll transition between early and late time de Sitter phases, both in the homogeneous case and in the presence of a black hole, in a scalar field model with a generic potential having both a maximum and a positive minimum. Asymptotically future de Sitter spacetimes are characterized by ADM charges known as cosmological tensions. We show that the late time de Sitter phase has finite cosmological tension when the scalar field oscillation around its minimum is underdamped, while the cosmological tension in the overdamped case diverges. We compute the variation in the cosmological and black hole horizon areas between the early and late time phases, finding that the fractional change in horizon area is proportional to the corresponding fractional change in the effective cosmological constant. We show that the extended first law of thermodynamics, including variation in the effective cosmological constant, is satisfied between the initial and final states, and discuss the dynamical evolution of the black hole temperature.