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

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.