Acceleration in de Sitter spacetimes

TL;DR

This paper introduces a new way to define uniformly accelerated frames in de Sitter spacetimes, generalizing the Rindler transformation to curved backgrounds using point-dependent isometries.

Contribution

It proposes a novel method to construct accelerated frames in de Sitter spaces that smoothly connect to the Rindler frames in flat spacetime, extending the concept to any dimension.

Findings

Defined uniform acceleration in de Sitter using Nachtmann coordinates

Derived a generalized Rindler transformation for de Sitter spacetimes

Ensured continuous dependence on acceleration in the flat limit

Abstract

We propose a definition of uniform accelerated frames in de Sitter spacetimes applying the Nachtmann method of introducing coordinates using suitable point-dependent isometries. In order to recover the well-known Rindler approach in the flat limit, we require the transformation between the static frame and the accelerated one to depend continuously on acceleration, obtaining thus the natural generalization of the Rindler transformation to the de Sitter spacetimes of any dimensions.