Relativistic rigid systems and the cosmic expansion

TL;DR

This paper investigates the conditions for rigidity in bodies within an expanding universe, introduces quasilocal rigidity, and explores implications for understanding cosmic expansion and gravitational energy.

Contribution

It establishes new theorems and definitions for rigidity in general spacetimes, including the novel concept of quasilocal rigidity, and applies these to cosmology.

Findings

Defined conditions for rigidity in expanding universes

Introduced the concept of quasilocal rigidity

Compared gravitational energy calculations with previous literature

Abstract

We analyze the necessary conditions for a body to remain rigid in an expanding cosmological Universe. First, we establish the main theorems and definitions for having a rigid body in a general spacetime as well as the new concept of quasilocal rigidity. We apply the obtained results to a homogeneous universe exploring the differences with flat spacetime. We discuss how the concept of rigid body helps to understand the expansion of space in cosmology. Finally, using a rigid system as a reference frame, we calculate the gravitational energy, and we compare it with previous results in the literature.