Black holes and stars in the Horava-Lifshitz theory with the projectability condition

Jared Greenwald, Antonios Papazoglou, and Anzhong Wang
Phys. Rev. D 81, 084046 – Published 26 April 2010

Abstract

We systematically study spherically symmetric static spacetimes filled with a fluid in the Horava-Lifshitz theory of gravity with the projectability condition, but without the detailed balance. We establish that when the spacetime is spatially Ricci flat the unique vacuum solution is the de Sitter Schwarzshcild solution, while when the spacetime has a nonzero constant curvature, there exist two different vacuum solutions; one is an (Einstein) static universe, and the other is a new spacetime. This latter spacetime is maximally symmetric and not flat. We find all the perfect fluid solutions for such spacetimes, in addition to a class of anisotropic fluid solutions of the spatially Ricci flat spacetimes. To construct spacetimes that represent stars, we investigate junction conditions across the surfaces of stars and obtain the general matching conditions with or without the presence of infinitely thin shells. It is remarkable that, in contrast to general relativity, the radial pressure of a star does not necessarily vanish on its surface even without the presence of a thin shell, due to the presence of high order derivative terms. Applying the junction conditions to our explicit solutions, we show that it is possible to match smoothly these solutions (all with nonzero radial pressures) to vacuum spacetimes without the presence of thin matter shells on the surfaces of stars.

  • Received 18 January 2010

DOI:https://doi.org/10.1103/PhysRevD.81.084046

©2010 American Physical Society

Authors & Affiliations

Jared Greenwald1,*, Antonios Papazoglou2,†, and Anzhong Wang1,‡

  • 1GCAP-CASPER, Physics Department, Baylor University, Waco, Texas 76798-7316, USA
  • 2Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, United Kingdom

  • *Jared_Greenwald@baylor.edu
  • antonios.papazoglou@port.ac.uk
  • anzhong_wang@baylor.edu

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Issue

Vol. 81, Iss. 8 — 15 April 2010

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