Equivalent teleparallel theories in diagonalizable spacetimes: Comment on "Metric-affine approach to teleparallel gravity"

TL;DR

This paper demonstrates that multiple teleparallel gravity models, beyond the teleparallel equivalent of general relativity, can admit vacuum solutions like black holes in diagonalizable spacetimes, challenging previous claims of uniqueness.

Contribution

It identifies a broader class of teleparallel models that admit vacuum solutions, showing that the teleparallel equivalent of general relativity is not the only such model.

Findings

Existence of a wider class of teleparallel models admitting vacuum solutions.

The teleparallel equivalent of general relativity is not unique in admitting black hole solutions.

Different approaches can reveal broader solution spaces in teleparallel gravity.

Abstract

It is well known that the teleparallel equivalent of general relativity yields the same vacuum solutions as general relativity does, which ensures that this particular teleparallel model is in good agreement with experiments. A less known result concerns the existence of a wider class of teleparallel models which also admits these solutions when the spacetime is diagonalizable by means of a coordinate change. However, it is stated in Ref. [Phys. Rev. D 67, 044016 (2003).] that the teleparallel equivalent of general relativity is the only teleparallel model which admits black holes. To show that this statement is not true, I prove the existence of this wider class by taking an approach different from that of Ref. [Phys. Rev. D 19, 3524 (1979)].