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Galaxies 2013, 1(3), 261-274; doi:10.3390/galaxies1030261
Article

A No-Go Theorem for Rotating Stars of a Perfect Fluid without Radial Motion in Projectable Hořava–Lifshitz Gravity

*  and
Department of Physics, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima-ku, Tokyo 171-8501, Japan
* Author to whom correspondence should be addressed.
Received: 16 October 2013 / Revised: 27 November 2013 / Accepted: 10 December 2013 / Published: 16 December 2013
(This article belongs to the Special Issue Aspects of Black Hole Physics)
Download PDF [123 KB, 19 December 2013; original version 16 December 2013]

Abstract

Hořava–Lifshitz gravity has covariance only under the foliation-preserving diffeomorphism. This implies that the quantities on the constant-time hypersurfaces should be regular. In the original theory, the projectability condition, which strongly restricts the lapse function, is proposed. We assume that a star is filled with a perfect fluid with no-radial motion and that it has reflection symmetry about the equatorial plane. As a result, we find a no-go theorem for stationary and axisymmetric star solutions in projectable Hořava–Lifshitz  gravity under the physically reasonable assumptions in the matter sector. Since we do not use the gravitational action to prove it, our result also works out in other projectable theories and applies to not only strong gravitational fields, but also weak gravitational ones.
Keywords: Hořava–Lifshitz gravity; projectable gravity; rotating star Hořava–Lifshitz gravity; projectable gravity; rotating star
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Tsukamoto, N.; Harada, T. A No-Go Theorem for Rotating Stars of a Perfect Fluid without Radial Motion in Projectable Hořava–Lifshitz Gravity. Galaxies 2013, 1, 261-274.

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