Generalizations of the Levi-Civita-Bertotti-Robinson spacetime

Abstract

The Levi-Civita-Bertotti-Robinson (LBR) solution of Einstein's field equations may be interpreted to describe spacetime in a region without matter outside a charged spherical domain wall. In the present paper we investigate the physical properties of some solutions of the Einstein-Maxwell equations, and show that they are generalizations of the LBR solution. One represents a spacetime with charged dust outside a charged shell, and another one a spacetime with Lorentz-Invariant Vacuum Energy (LIVE) outside a charged shell. The uniqueness of static, spherically symmetric and conformally flat solutions of the Einstein-Maxwell field equations is also discussed.