Maximally extended, explicit and regular coverings of the Schwarzschild - de Sitter vacua in arbitrary dimension

TL;DR

This paper presents new, explicit coordinate systems for the Schwarzschild-de Sitter vacua in arbitrary dimensions, providing more regular and comprehensive spacetime coverings than traditional methods like Kruskal-Szekeres.

Contribution

It introduces maximally extended, explicit, and regular coordinate coverings for Schwarzschild-de Sitter spacetimes in any dimension, improving upon existing methods.

Findings

New coordinate systems cover the entire spacetime manifold.

Coordinates are explicit and regular, avoiding singularities.

Applicable to all dimensions with a spherical symmetry.

Abstract

Maximally extended, explicit and regular coverings of the Schwarzschild - de Sitter family of vacua are given, first in spacetime (generalizing a result due to Israel) and then for all dimensions $D$ (assuming a $D-2$ sphere). It is shown that these coordinates offer important advantages over the well known Kruskal - Szekeres procedure.