Gravitational collapse in Ho\v{r}ava-Lifshitz theory

TL;DR

This paper investigates gravitational collapse in Hořava-Lifshitz gravity, deriving junction conditions and analyzing external spacetimes, revealing differences from general relativity depending on the coupling constant λ.

Contribution

It provides the first detailed analysis of gravitational collapse and junction conditions in Hořava-Lifshitz gravity with arbitrary λ, extending understanding of stellar dynamics in this theory.

Findings

For λ=1, external spacetime is Schwarzschild (anti-) de Sitter in Painlevé-Gullstrand coordinates.

For λ≠1, external spacetime is static but not asymptotically flat.

Junction conditions are derived for collapsing stars with perfect fluid and vacuum exterior.

Abstract

We study gravitational collapse of a spherical fluid in nonrelativistic general covariant theory of the Ho\v{r}ava-Lifshitz gravity 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 distribution theory. 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. If the perfect fluid is pressureless (a dust fluid), it is found that the matching is also possible. In particular, in the case $\lambda = 1$, the external spacetime is described by the Schwarzschild (anti-) de Sitter solution written in Painlev\'e-Gullstrand coordinates. In the case $\lambda \not= 1$, the external spacetime is static but not asymptotically flat. Our treatment can be easily generalized to other versions of Ho\v{r}ava-Lifshitz gravity or, more generally, to any theory of higher-order derivative gravity.