Batalin-Fradkin-Vilkovisky quantization of Einstein gravity with off-diagonal solutions encoding Ho\v{r}ava type generating functions

TL;DR

This paper develops a BFV quantization method for off-diagonal Einstein gravity solutions that encode Hořava-Lifshitz configurations, revealing their nonlinear symmetries and anisotropic scaling in a quantum gravity context.

Contribution

It introduces a novel BFV formalism tailored for off-diagonal solutions in Einstein gravity that incorporate Hořava-Lifshitz features, expanding quantization techniques.

Findings

Quantization of off-diagonal Einstein solutions with HL properties.

Identification of nonlinear symmetries in quasi-classical quantum gravity.

Geometric constructions on Lorentz manifolds with nonholonomic fibrations.

Abstract

We develop and apply the Batalin-Fradkin-Vilkovisky (BFV) formalism for quantizing off-diagonal solutions of the Einstein equations in general relativity. In the quasi-classical limit of quantum gravity, such solutions possess specific nonlinear symmetries and encode Ho\v{r}ava - Lifshitz (HL) configurations with anisotropic scaling and effective cosmological constants. The geometric constructions are performed on Lorentz manifolds enabled with nonholonomic 2+2 and 3+1 fibration structures.