Black Plane Solutions and Localized Gravitational Energy

We explore the issue of gravitational energy localization for static plane-symmetric solutions of the Einstein-Maxwell equations in 3+1 dimensions with asymptotic anti-de Sitter behavior. We apply three different energy-momentum complexes, the Einstein, Landau-Lifshitz, and Møller prescriptions, to the metric representing this category of solutions and determine the energy distribution for each. We find that the three prescriptions offer identical energy distributions, suggesting their utility for this type of model.

ENERGY DISTRIBUTION OF BLACK PLANE SOLUTIONS

We use the Einstein energy–momentum complex to calculate the energy distribution of static plane-symmetric solutions of the Einstein–Maxwell equations in 3+1 dimensions with asymptotic anti-de Sitter behavior. This solution is expressed in terms of three parameters: the mass, electric charge and cosmological constant. We compare the energy distribution to that of the Reissner–Nordström–anti-de Sitter solution, pointing to qualitative differences between the models. Finally, we examine these results within the context of the Cooperstock hypothesis.

Null Fluid Collapse in the Plane Symmetric Anti-de Sitter Spacetime

The stability of the plane anti-de Sitter spacetime and the gravitational collapse in the plane symmetric anti-de Sitter spacetime are investigated. A scalar curvature singularity will be formed at the r=0 plane when the anti-de Sitter spacetime is perturbed by null dust. By employing the method suggested recently by Husain we find a family of non-static exact solution of the null fluid collapse with equation of state P=kρ in the plane anti-de Sitter spacetime. The late time limit of the solutions results in a black plane solution possessing multiple horizon structure.