General Relativity and Gravitation

, Volume 44, Issue 7, pp 1769–1786 | Cite as

Higher-dimensional perfect fluids and empty singular boundaries

  • Ricardo E. Gamboa Saraví
Research Article


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 ρ = ηp, being η an arbitrary constant and N ≥ 2. We show that this spacetime has some weird properties. In particular, in the case η > −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 η > 1, we find that only vertical null geodesics touch the boundary and bounce, and all of them start and finish at z = ∞; 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.


Gravitation Singularities Higher-dimensional spacetimes 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Departamento de Física, Facultad de Ciencias ExactasUniversidad Nacional de La PlataLa PlataArgentina
  2. 2.IFLP, CONICETLa PlataArgentina

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