1204.4907 (Ricardo E. Gamboa Saravi)

Higher-dimensional perfect fluids and empty singular boundaries    [PDF]

Ricardo E. Gamboa Saravi

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 $N\geq2$. 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.

View original: http://arxiv.org/abs/1204.4907