Jared Greenwald, Jonatan Lenells, V. H. Satheeshkumar, Anzhong Wang
We study gravitational collapse of a spherical fluid in Ho\v{r}ava-Lifshitz theory with the projectability condition and an arbitrary coupling constant $\lambda$, where $|\lambda - 1|$ characterizes the deviation of the theory from general relativity in the infrared limit. The junction conditions across the surface of a collapsing star are derived under the (minimal) assumption that the junctions be mathematically meaningful in terms of generalized functions. When the collapsing star is made of a homogeneous and isotropic perfect fluid, {and} the external region is described by a stationary spacetime, the problem reduces to the matching of six independent conditions. When the perfect fluid is pressureless (a dust fluid), it is found that such matching is possible only in the case $\lambda = 1$. In this case, the external spacetime is described by the Schwarzschild (anti-) de Sitter solution written in Painlev\'e-Gullstrand coordinates. Our treatment can be easily generalized to other versions of Ho\v{r}ava-Lifshitz gravity or, more generally, to any model of a higher-order derivative gravity theory.
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http://arxiv.org/abs/1304.1167
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