Generalized De Sitter Space

TL;DR

This paper introduces a broader class of solutions to Einstein's equations that generalize de Sitter space, explores their global structure and thermal properties, and examines their stability under perturbations.

Contribution

It presents new two-parameter solutions to Einstein's equations that extend de Sitter space and analyzes their global structure, thermal characteristics, and stability.

Findings

Generalized solutions are more comprehensive than de Sitter space.

The thermal properties are consistent with Euclidean methods.

The solutions are stable under specific perturbations.

Abstract

This paper deals with some two-parameter solutions to the spherically symmetric, vacuum Einstein equations which, we argue, are more general than de Sitter solution. The global structure of one such spacetimes and its extension to the multiply connected case have also been investigated. By using a six-dimensional Minkowskian embedding as its maximal extension, we check that the thermal properties of the considered solution in such an embedding space are the same as those derived by the usual Euclidean method. The stability of the generalized de Sitter space containing a black hole has been investigated as well by introducing perturbations of the Ginsparg-Perry type in first order approximation. It has been obtained that such a space perdures against the effects of these perturbations.