Empty singularities in higher-dimensional Gravity

Abstract

We study the exact solution of Einstein's field equations consisting of a ($n+2$)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density $\rho$ and thickness $d$, surrounded by two different vacua. We explicitly write down the pressure and the external gravitational fields in terms of $\rho$ and $d$, the pressure is positive and bounded, presenting a maximum at an asymmetrical position. And if $\sqrt{\rho }d$ is small enough, the dominant energy condition is satisfied all over the spacetime. We find that this solution presents many interesting features. In particular, it has an empty singular boundary in one of the vacua.

arXiv comment13 pages

References in corpus (8)

• Large N Field Theories, String Theory and Gravity
• Brane-World Gravity
• Black Holes in Higher Dimensions
• Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime
• Infinite slabs and other weird plane symmetric space-times with constant positive density
• The white wall, a gravitational mirror
• The Gravitational Field of a Plane Slab
• An alternative well-posedness property and static spacetimes with naked singularities

Cited by in corpus (1)

• Plane symmetric gravitational fields in (D+1)-dimensional General Relativity