Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity

TL;DR

This paper introduces a contraction method using multiple Poincaré algebra copies to derive non-relativistic and ultra-relativistic limits of multimetric gravity theories, connecting them to Newtonian gravity formulations.

Contribution

It provides a novel contraction technique to reconstruct extended non-relativistic and ultra-relativistic algebras and their action principles from multimetric gravity.

Findings

Derived non-relativistic limit of bi-metric gravity.

Connected contraction limits to Newtonian gravity with background density.

Presented a systematic method for obtaining gravity limits from Poincaré algebra multiples.

Abstract

We present a method of contraction that can be applied to re-construct the recent extended non-relativistic and ultra-relativistic algebras as well as corresponding action principles. The methodology involves the use of multiple copies of Poincar\'e algebra. Consequently, the contraction defines non-relativistic or ultra-relativistic limits of multimetric theories of gravity. In particular, we show that the non-relativistic scaling limit of bi-metric gravity corresponds to the recent formulation of an action principle for Newtonian gravity with a constant background mass density.