Entropy in locally-de Sitter spacetimes

TL;DR

This paper explores how the concepts of energy and entropy are modified in de Sitter spacetimes, especially when considering black holes, horizons, and their entanglement, impacting cosmological models.

Contribution

It introduces a new perspective on entropy and energy in de Sitter spacetimes, emphasizing the role of horizon entanglement and its implications for cosmology.

Findings

Black hole and de Sitter horizons form an entangled system.

Energy conservation constrains black hole activity and de Sitter radius evolution.

Modified notions of diffeomorphism affect entropy and energy definitions.

Abstract

As quotient spaces, Minkowski and de Sitter are fundamental spacetimes in the sense that they are known "a priori", independently of Einstein equation. They represent different non-gravitational backgrounds for the construction of physical theories. If general relativity is constructed on a de Sitter spacetime, the underlying kinematics will no longer be ruled by Poincar\'e, but by the de Sitter group. In this case the definition of diffeomorphism changes, producing concomitant changes in the notions of energy and entropy. These changes are explicitly discussed for the case of the Schwarzschild solution, in which the black hole and the de Sitter horizons show up as a unique entangled system. Such entanglement, together with energy conservation, create a constraint between the black hole activity and the evolution of the de Sitter radius, providing a new scenario for the study of cosmology.