Higher-dimensional perfect fluids and empty singular boundaries

Abstract

In order to find out whether empty singular boundaries can arise in higher dimensional Gravity, we study the solution of Einstein's equations consisting in a ($N+2$)-dimensional static and hyperplane symmetric perfect fluid satisfying the equation of state $\rho =\eta p$, being $\rho$ an arbitrary constant and $N\ge 2$. We show that this spacetime has some weird properties. In particular, in the case $\eta >-1$, it has an empty (without matter) repulsive singular boundary. We also study the behavior of geodesics and the Cauchy problem for the propagation of massless scalar field in this spacetime. For $\eta >1$, we find that only vertical null geodesics touch the boundary and bounce, and all of them start and finish at $z=\infty$; whereas non-vertical null as well as all time-like ones are bounded between two planes determined by initial conditions. We obtain that the Cauchy problem for the propagation of a massless scalar field is well-posed and waves are completely reflected at the singularity, if we only demand the waves to have finite energy, although no boundary condition is required.

arXiv comment16 pages

References in corpus (6)

• Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime
• Static plane symmetric relativistic fluids and empty repelling singular boundaries
• The white wall, a gravitational mirror
• Infinite slabs and other weird plane symmetric space-times with constant positive density
• The Gravitational Field of a Plane Slab
• An alternative well-posedness property and static spacetimes with naked singularities

Cited by in corpus (3)

• Exact plane symmetric black bounce with a perfect-fluid exterior obeying a linear equation of state
• Plane symmetric gravitational fields in (D+1)-dimensional General Relativity
• Planar black holes and wormholes with a flat exterior