On spectral geometry approach to Horava-Lifshitz gravity: Spectral dimension

TL;DR

This paper applies spectral geometry to Horava-Lifshitz gravity, calculating the spectral dimension of space-time and confirming Horava's results for various geometries, offering a new analytical framework.

Contribution

It introduces a spectral geometry approach to Horava-Lifshitz gravity, reproducing the spectral dimension results for arbitrary non-flat space-times.

Findings

Spectral dimension matches Horava's predictions.

Method applies to non-flat space-times.

Framework respects foliation and anisotropic scaling.

Abstract

We initiate the study of Horava-Lifshitz models of gravity in the framework of spectral geometry. As the first step, we calculate the dimension of space-time. It is shown, that for the natural choice of a Dirac operator (or rather corresponding generalized Laplacian), which respects both the foliation structure and anisotropic scaling, the result of Horava on a spectral dimension is reproduced for an arbitrary, non-flat space-time. The advantage and further applications of our approach are discussed.