Static electromagnetic fields and charged black holes in general covariant theory of Horava-Lifshitz gravity

TL;DR

This paper explores static electromagnetic solutions in Horava-Lifshitz gravity, revealing black hole solutions with horizons that depend on test particle energies, differing fundamentally from general relativity due to high-order momentum effects.

Contribution

It provides the first complete set of electric static solutions in HL gravity, generalizing Reissner-Nordstrom black holes and analyzing their horizon structures under high-energy particle effects.

Findings

Some solutions describe charged black holes with energy-dependent horizons.

Test particles do not follow geodesics due to high-order momentum terms.

The spacetime structure differs from GR, affecting black hole properties.

Abstract

In this paper, we study electromeganetic static spacetimes in the nonrelativisitc general covariant theory of the Horava-Lifshitz (HL) gravity, proposed recently by Horava and Melby-Thompson, and present all the electric static solutions, which represent the generalization of the Reissner-Nordstrom solution found in Einstein's general relativity (GR). The global/local structures of spacetimes in the HL theory in general are different from those given in GR, because the dispersion relations of test particles now contain high-order momentum terms, so the speeds of these particles are unbounded in the ultraviolet (UV). As a result, the conception of light-cones defined in GR becomes invalid and test particles do not follow geodesics. To study black holes in the HL theory, we adopt the geometrical optical approximations, and define a horizon as a (two-closed) surface that is free of spacetime singularities and on which massless test particles are infinitely redshifted. With such a definition, we show that some of our solutions give rise to (charged) black holes, although the radii of their horizons in general depend on the energies of the test particles.