paper

Shear-free Dust Solution in General Covariant Hořava-Lifshitz Gravity

arXiv:1509.02685 · doi:10.1007/s10714-015-2013-2

Abstract

In this paper, we have studied non stationary dust spherically symmetric spacetime, in general covariant theory ( extension) of the Hořava-Lifshitz gravity with the minimally coupling and non-minimum coupling with matter, in the post-newtonian approximation (PPN) in the infrared limit. The Newtonian prepotential was assumed null. The aim of this work is to know if we can have the same spacetime, as we know in the General Relativity Theory (GRT), in Hořava-Lifshitz Theory (HLT) in this limit. We have shown that there is not an analogy of the dust solution in HLT with the minimally coupling, as in GRT. Using non-minimum coupling with matter, we have shown that the solution admits a process of gravitational collapse, leaving a singularity at the end. This solution has, qualitatively, the same temporal behaviour as the dust collapse in GRT. However, we have also found a second possible solution, representing a bounce behavior that is not found in GRT.

arXiv comment12 pages and 1 figure. arXiv admin note: substantial text overlap with arXiv:1412.5045. Accepted for publication in Gen. Rel. Grav

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