On Effective Spacetime Dimension in the Ho\v{r}ava-Lifshitz Gravity

TL;DR

This paper investigates the effective spacetime dimension in Hořava-Lifshitz gravity, confirming dimensional reduction to 2 in the ultraviolet and 4 in the infrared, and explores implications for thermodynamics and gravitational effects.

Contribution

It explicitly computes the effective spacetime dimension in Hořava-Lifshitz gravity backgrounds and analyzes thermodynamic and gravitational consequences, including constraints from solar radiance data.

Findings

Spacetime effectively reduces to 2 dimensions at high energies.

Spacetime remains 4-dimensional at low energies.

Gravity modifies thermodynamic laws and forces near black bodies.

Abstract

In this manuscript we explicitly compute the effective dimension of spacetime in some backgrounds of Ho\v{r}ava-Lifshitz (H-L) gravity. For all the cases considered, the results are compatible with a dimensional reduction of the spacetime to $d+1=2$, at high energies (ultraviolet limit), which is confirmed by other quantum gravity approaches, as well as to $d+1=4$, at low energies (infrared limit). This is obtained by computing the free energy of massless scalar and gauge fields. We find that the only effect of the background is to change the proportionality constant between the internal energy and temperature. Firstly, we consider both the non-perturbative and perturbative models involving the matter action, without gravitational sources but with manifest time and space symmetry breaking, in order to calculate modifications in the Stephan-Boltzmann law. When gravity is taken into account, we assume a scenario in which there is a spherical source with mass $M$ and radius $R$ in thermal equilibrium with radiation, and consider the static and spherically symmetric solution of the H-L theory found by Kehagias-Sfetsos (K-S), in the weak and strong field approximations. As byproducts, for the weak field regime, we used the current uncertainty of the solar radiance measurements to establish a constraint on the $\omega$ free parameter of the K-S solution. We also calculate the corrections, due to gravity, to the recently predicted attractive force that black bodies exert on nearby neutral atoms and molecules.