Generalized Teleparallel de Sitter geometries

TL;DR

This paper explores teleparallel geometries that generalize de Sitter spaces, focusing on affine symmetries, Einstein teleparallel geometries, and presenting explicit solutions within this framework.

Contribution

It introduces a classification of teleparallel de Sitter geometries with affine symmetries and provides explicit exact solutions, expanding understanding of teleparallel gravity models.

Findings

Classification of teleparallel de Sitter geometries with affine symmetries

Identification of two one-parameter families of explicit solutions

Analysis of Einstein teleparallel geometries with Lie algebra symmetries

Abstract

Theories of gravity based on teleparallel geometries are characterized by the torsion, which is a function of the coframe, derivatives of the coframe, and a zero curvature and metric compatible spin connection. The appropriate notion of a symmetry in a teleparallel geometry is that of an affine symmetry. Due to the importance of the de Sitter geometry and Einstein spaces within general relativity, we shall describe teleparallel de Sitter geometries and discuss their possible generalizations. In particular, we shall analyse a class of Einstein teleparallel geometries which have a 4-dimensional Lie algebra of affine symmetries, and display two one-parameter families of explicit exact solutions.