Evolving Black Holes in Inflation

TL;DR

This paper derives an analytic perturbative solution to Einstein's equations with a scalar field, modeling dynamical black holes during slow-roll inflation, revealing horizon area growth and thermodynamic law satisfaction.

Contribution

It provides a novel analytic, perturbative framework for evolving black holes in inflationary cosmology, linking horizon dynamics with scalar potential evolution.

Findings

Black hole and cosmological horizon areas increase over time.

Horizon area change proportional to the change in cosmological constant.

Thermodynamic laws are satisfied throughout the evolution.

Abstract

We present an analytic, perturbative solution to the Einstein equations with a scalar field that describes dynamical black holes in a slow-roll inflationary cosmology. We show that the metric evolves quasi-statically through a sequence of Schwarzschild-de Sitter like metrics with time dependent cosmological constant and mass parameters, such that the cosmological constant is instantaneously equal to the value of the scalar potential. The areas of the black hole and cosmological horizons each increase in time as the effective cosmological constant decreases, and the fractional area increase is proportional to the fractional change of the cosmological constant, times a geometrical factor. For black holes ranging in size from much smaller than to comparable to the cosmological horizon, the pre-factor varies from very small to order one. The "mass first law" and the "Schwarzschild-de Sitter patch first law" of thermodynamics are satisfied throughout the evolution.