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

Galaxies

Naoki Tsukamoto¹ 

关键词: Hořava–Lifshitz gravity;    projectable gravity;    rotating star;   

DOI  :  10.3390/galaxies1030261

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.