Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2012-01-09
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
15 pages, no figures
Scientific paper
Ho\v{r}ava-Lifshitz gravity has covariance only under the foliation-preserving diffeomorphism. This implies that the quantities on the constant-time hypersurfaces should be regular. In this theory, the projectability condition which strongly restricts the lapse function is required. We assume that a star is filled with a perfect fluid, that it has the reflection symmetry about the equatorial plane. As a result, we find that there are no stationary axisymmetric star solutions in Ho\v{r}ava-Lifshitz gravity under the physically reasonable assumptions on the matter sector. This is a serious problem in this theory from the view point of astrophysics. It seems that the invariance under the foliation-preserving diffeomorphism and the projectability condition are questionable since our result is derived from them.
Harada Tomohiro
Tsukamoto Naoki
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