Black holes, compact objects and solar system tests in non-relativistic general covariant theory of gravity

TL;DR

This paper investigates static spherically symmetric spacetimes in a nonrelativistic covariant gravity theory, revealing unique vacuum solutions constrained by solar system tests and enabling the construction of non-singular static stars with specific junction conditions.

Contribution

It provides new solutions for static stars in nonrelativistic covariant gravity, including non-singular configurations and detailed junction conditions, expanding understanding beyond previous models.

Findings

Vacuum solutions are non-unique and depend on the U(1) gauge field A.

Solar system tests constrain A, favoring the Schwarzschild solution.

Non-singular static stars with perfect fluid can be constructed in this theory.

Abstract

We study spherically symmetric static spacetimes generally filled with an anisotropic fluid in the nonrelativistic general covariant theory of gravity. In particular, we find that the vacuum solutions are not unique, and can be expressed in terms of the $U(1)$ gauge field $A$. When solar system tests are considered, severe constraints on $A$ are obtained, which seemingly pick up the Schwarzschild solution uniquely. In contrast to other versions of the Horava-Lifshitz theory, non-singular static stars made of a perfect fluid without heat flow can be constructed, due to the coupling of the fluid with the gauge field. These include the solutions with a constant pressure. We also study the general junction conditions across the surface of a star. In general, the conditions allow the existence of a thin matter shell on the surface. When applying these conditions to the perfect fluid solutions with the vacuum ones as describing their external spacetimes, we find explicitly the matching conditions in terms of the parameters appearing in the solutions. Such matching is possible even without the presence of a thin matter shell.