Stellar center is dynamical in Horava-Lifshitz gravity

TL;DR

In Horava-Lifshitz gravity, the regularity conditions at a star's center imply that static, spherically symmetric stars cannot exist without a time-dependent core, highlighting fundamental differences from general relativity.

Contribution

The paper proves that regular static stars cannot exist in Horava-Lifshitz gravity, requiring a time-dependent region at the center, regardless of higher curvature terms or critical exponent z.

Findings

Static spherically symmetric stars are incompatible with regularity conditions.

A time-dependent core region is necessary at the star's center.

The result holds for any dynamical critical exponent z.

Abstract

In Horava-Lifshitz gravity, regularity of a solution requires smoothness of not only the spacetime geometry but also the foliation. As a result, the regularity condition at the center of a star is more restrictive than in general relativity. Assuming that the energy density is a piecewise-continuous, non-negative function of the pressure and that the pressure at the center is positive, we prove that the momentum conservation law is incompatible with the regularity at the center for any spherically-symmetric, static configurations. The proof is totally insensitive to the structure of higher spatial curvature terms and, thus, holds for any values of the dynamical critical exponent $z$. Therefore, we conclude that a spherically-symmetric star should include a time-dependent region near the center. We also comment on the condition under which linear instability of the scalar graviton does not show up.