Spherically symmetric solutions of gravitation equations on the background with spatial sections of constant curvature

TL;DR

This paper explores spherically symmetric solutions to Einstein's equations on curved backgrounds with constant curvature spatial sections, revealing new wormhole solutions and connections to classical black hole solutions.

Contribution

It introduces and analyzes new spherically symmetric solutions on curved backgrounds, including wormholes, extending classical solutions like Schwarzschild and Reissner-Nordström.

Findings

Two solution branches: classical black holes and wormholes.

Wormhole solutions have no Einstein limit.

Solutions reduce to known black holes in flat background limit.

Abstract

We investigate the vacuum and charged spherically symmetric static solutions of the Einstein equations on cosmological background. The background metric is not flat, but curved, with constant - curvature spatial sections. Both vacuum and charged cases contain two branches. The first branches transform into the Schwarzschild and Reissner-Nordstr\"om solutions if the background metric goes to the Minkovski one. The second branches describe wormholes and have no Einstein limit.