Charged Throats in the Hořava--Lifshitz Theory

Abstract

A spherically symmetric solution of the field equations of the Hořava-Lifshitz gravity-gauge vector interaction theory is obtained and analyzed. It describes a charged throat. The solution exists provided a restriction on the relation between the mass and charge is satisfied. The restriction reduces to the Reissner-Nordström one in the limit in which the coupling constants tend to the relativistic values of General Relativity. We introduce the correct charts to describe the solution across the entire manifold, including the throat connecting an asymptotic Minkowski space-time with a singular 3+1 dimensional manifold. The solution external to the throat on the asymptotically flat side tends to the Reissner-Nordström space-time at the limit when the coupling parameter, associated with the term in the low energy Hamiltonian that manifestly breaks the relativistic symmetry, tends to zero. Also, when the electric charge is taken to be zero the solution becomes the spherically symmetric and static solution of the Hořava-Lifshitz gravity.

Wave zone of the Hořava--Lifshitz gravity coupled to a gauge vector

“…Static and spherically symmetric solutions of the Hořava-Lifshitz field equations in the context of the non-projectable version have been found. Particularly, these solutions correspond to wormhole throats [46][47][48], although in the projectable version [49] and in 2D [50] wormholes structures were obtained. Concerning the experimental challenges, recent detection of gravitational waves [4,5] restricts the coupling parameter α and β (both appearing in the potential in the low energy regime z = 1).…”

Gravitational waves in Hořava-Lifshitz anisotropic gravity

“…Although at the linearized level Hořava-Lifshitz theory and GR coincide, the full theories behave in a different way as can be seen from the static spherical symmetric solutions of the field equations. In this case, in the Hořava-Lifshitz theory there are solutions with a throat, connecting an asymptotically flat manifold with a nonasymptotically flat one [27], see also [28] where a charged throat is considered. The solutions depend in one coupling constant α in a way that in the limit when α → 0 the geometry outside the throat , on the asymtotically flat side, tends to the geometry of the Schwarzchild solutions in GR outside the black hole.…”