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

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.