Gravitational collapse in Hořava-Lifshitz theory

Jared Greenwald, Jonatan Lenells, V. H. Satheeshkumar, and Anzhong Wang
Phys. Rev. D 88, 024044 – Published 24 July 2013

Abstract

We study gravitational collapse of a spherical fluid in nonrelativistic general covariant theory of the Hořava-Lifshitz gravity with the projectability condition and an arbitrary coupling constant λ, where |λ1| 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 λ=1, the external spacetime is described by the Sch–(anti–)de Sitter solution written in Painlevé-Gullstrand coordinates. In the case λ1, the external spacetime is static but not asymptotically flat. Our treatment can be easily generalized to other versions of Hořava-Lifshitz gravity or, more generally, to any theory of higher-order derivative gravity.

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  • Received 7 April 2013

DOI:https://doi.org/10.1103/PhysRevD.88.024044

© 2013 American Physical Society

Authors & Affiliations

Jared Greenwald1,*, Jonatan Lenells2,3,†, V. H. Satheeshkumar1,‡, and Anzhong Wang1,4,§

  • 1Physics Department, GCAP-CASPER, Baylor University, Waco, Texas 76798-7316, USA
  • 2Department of Mathematics, Baylor University, Waco, Texas 76798-7328, USA
  • 3Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom
  • 4Institute for Advanced Physics Mathematics, Zhejiang University of Technology, Hangzhou 310032, China

  • *Jared_Greenwald@baylor.edu
  • Jonatan_Lenells@baylor.edu
  • VH_Satheeshkumar@baylor.edu
  • §Anzhong_Wang@baylor.edu

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Vol. 88, Iss. 2 — 15 July 2013

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