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

TL;DR

This paper explores spherically symmetric solutions in Horava-Lifshitz gravity with projectability, revealing unique vacuum solutions, fluid configurations, and star models with nonzero surface pressures, differing from general relativity.

Contribution

It provides a systematic classification of solutions, including new spacetimes and star models, within Horava-Lifshitz gravity without detailed balance, highlighting differences from general relativity.

Findings

Unique vacuum solutions for Ricci flat and curved spacetimes.

Existence of non-flat, maximally symmetric vacuum spacetime.

Star models with nonzero radial pressure at the surface, matching smoothly to vacuum without thin shells.

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.