Isotropic extensions of the vacuum solutions in general relativity

TL;DR

This paper develops isotropic extensions of spherically symmetric vacuum solutions in general relativity, deriving exact and perturbative geometries including black holes, wormholes, and anti-de Sitter spaces, with broad applicability.

Contribution

It introduces a method to generate isotropic extensions of vacuum solutions, expanding the set of known geometries in general relativity.

Findings

Derived new classes of black hole solutions in compact and noncompact universes.

Constructed wormhole geometries within cosmological horizons.

Explored anti-de Sitter geometries with angular excess or deficit.

Abstract

In this work, we obtain isotropic extensions of the usual spherically symmetric vacuum geometries in general relativity. Exact and perturbative solutions are derived. The classes of geometries obtained include black holes in compact and noncompact universes, wormholes in the interior region of cosmological horizons, and anti-de Sitter geometries with excess/deficit solid angle. The tools developed here are applicable in more general contexts.