Non-geodesic timelike observers and the ultralocal limit

TL;DR

This paper explores the limitations of the ultralocal limit along timelike geodesics, showing it does not generally apply to non-geodesic observers, with specific exceptions discussed.

Contribution

It identifies conditions under which the ultralocal limit extends to non-geodesic observers, including special cases like variable mass particles and scalar-tensor gravity.

Findings

Ultralocal limit reduces to Bianchi I for geodesic observers.

Extension to non-geodesic observers is generally not possible.

Exceptions include particles with variable mass and certain scalar-tensor theories.

Abstract

The ultralocal limit along timelike geodesics, in which any geometry reduces to Bianchi I, does not extend to non-geodesic timelike observers. Exceptions are discussed, including particles with variable mass, test particles in Einstein frame scalar-tensor gravity, and self-interacting dark matter.