Ricci curvature and metric in causal spacetimes

TL;DR

This paper demonstrates that in causal spacetimes, any diffeomorphism preserving Ricci curvature must be a homothety if the spacetime admits a complete timelike geodesic, linking curvature invariance to geometric symmetry.

Contribution

It establishes a new rigidity result connecting Ricci-preserving diffeomorphisms to homotheties in viable causal spacetimes.

Findings

Ricci-preserving causal diffeomorphisms are homotheties in viable spacetimes

Complete timelike geodesics characterize viability in the context of Ricci curvature

The result links curvature invariance to geometric symmetry in causal spacetimes

Abstract

A viable spacetime is one that admits a complete timelike geodesic. It is shown that a causal diffeomorphism preserving the Ricci tensor between two spacetimes is necessarily a homothety, if one of them is viable.