Complete Classification of Four-Dimensional Black Hole and Membrane Solutions in IR-modified Ho\v{r}ava Gravity

TL;DR

This paper classifies all static black hole and membrane solutions in IR-modified Hořava gravity, revealing unique singularity structures and their relation to non-singular cosmologies, and discusses conditions for recovering general relativity in the IR.

Contribution

It provides a complete classification of static solutions in IR-modified Hořava gravity, including new singularity types and the conditions for GR limit recovery.

Findings

Existence of surface-like curvature singularities at finite radius.

Milder divergence of singularities compared to general relativity.

Identification of a 'GR flow limit' for IR to GR transition.

Abstract

Ho\v{r}ava gravity has been proposed as a renormalizable, higher-derivative gravity without ghost problems, by considering different scaling dimensions for space and time. In the non-relativistic higher-derivative generalization of Einstein gravity, the meaning and physical properties of black hole and membrane space-times are quite different from the conventional ones. Here, we study the singularity and horizon structures of such geometries in IR-modified Ho\v{r}ava gravity, where the so-called "detailed balance" condition is softly broken in IR. We classify all the viable static solutions without naked singularities and study its close connection to non-singular cosmology solutions. We find that, in addition to the usual point-like singularity at $r=0$, there exists a "surface-like" curvature singularity at finite $r=r_S$ which is the cutting edge of the real-valued space-time. The degree of divergence of such singularities is milder than those of general relativity, and the Hawking temperature of the horizons diverges when they coincide with the singularities. As a byproduct we find that, in addition to the usual "asymptotic limit," a consistent flow of coupling constants, that we called "GR flow limit," is needed in order to recover general relativity in the IR.