https://doi.org/10.1140/epjc/s10052-022-10922-9
Regular Article - Theoretical Physics
Coincident gauge for static spherical field configurations in symmetric teleparallel gravity
1
Department of Physics, Tokyo Institute of Technology, 1-12-1 Ookayama, Meguro-ku, 152-8551, Tokyo, Japan
2
Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411, Tartu, Estonia
Received:
4
September
2022
Accepted:
13
October
2022
Published online:
29
October
2022
In symmetric teleparallel gravities, where the independent connection is characterized by nonmetricity while curvature and torsion are zero, it is possible to find a coordinate system whereby the connection vanishes globally and covariant derivatives reduce to partial derivatives – the coincident gauge. In this paper we derive general transformation rules into the coincident gauge for spacetime configurations where the both the metric and connection are static and spherically symmetric, and write out the respective form of the coincident gauge metrics. Taking different options in fixing the freedom in the connection allowed by the symmetry and the field equations, the Schwarzschild metric in the coincident gauge can take for instance the Cartesian, Kerr–Schild, and diagonal (isotropic-like) forms, while the BBMB black hole metric in symmetric teleparallel scalar–tensor theory a certain diagonal form fits the coincident gauge requirements but the Cartesian and Kerr–Schild forms do not. Different connections imply different value for the boundary term which could in principle be physically relevant, but simple arguments about the coincident gauge do not seem to be sufficient to fix the connection uniquely. As a byproduct of the investigation we also point out that only a particular subset of static spherically symmetric connections has vanishing nonmetricity in the Minkowski limit.
© The Author(s) 2022
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.