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

Understand

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.