Solutions of multigravity theories and discretized brane worlds

TL;DR

This paper explores solutions to 5D Einstein gravity with a discretized fifth dimension, revealing novel solutions with no continuum equivalents, including a Randall-Sundrum type metric without brane sources and models with continuous graviton mass spectra.

Contribution

It systematically analyzes how different discretization schemes affect solutions in multigravity theories, uncovering new solutions and properties not present in the continuum limit.

Findings

Discretization can produce Randall-Sundrum type metrics without brane sources.

Some solutions have no continuum counterpart, including signature changes and singularity avoidance.

Models exhibit a continuous graviton mass spectrum with 4D-like interactions at small scales.

Abstract

We determine solutions to 5D Einstein gravity with a discrete fifth dimension. The properties of the solutions depend on the discretization scheme we use and some of them have no continuum counterpart. In particular, we find that the neglect of the lapse field (along the discretized direction) gives rise to Randall-Sundrum type metric with a negative tension brane. However, no brane source is required. We show that this result is robust under changes in the discretization scheme. The inclusion of the lapse field gives rise to solutions whose continuum limit is gauge fixed by the discretization scheme. We find however one particular scheme which leads to an undetermined lapse reflecting the reparametrization invariance of the continuum theory. We also find other solutions, with no continuum counterpart with changes in the metric signature or avoidance of singularity. We show that the models allow a continuous mass spectrum for the gravitons with an effective 4D interaction at small scales. We also discuss some cosmological solutions.