Cotton gravity is not predictive
General Relativity and Quantum Cosmology
2024-08-14 v3 Cosmology and Nongalactic Astrophysics
High Energy Physics - Theory
Abstract
It is well-known that the theory of Cotton gravity proposed by Harada is trivially solved by all isotropic and homogeneous cosmologies. We show that this under-determination is more general. More precisely, the degree of arbitrariness in the solutions increases with the degree of symmetry. We give two simple examples. The first is that of static spherically symmetric solutions, which depend on an arbitrary function of the radial coordinate. The second is that of anisotropic cosmologies, which depend on an arbitrary function of time.
Keywords
Cite
@article{arxiv.2312.17662,
title = {Cotton gravity is not predictive},
author = {Gérard Clément and Khireddine Nouicer},
journal= {arXiv preprint arXiv:2312.17662},
year = {2024}
}
Comments
11 pages, revised augmented version, incorporates input from arXiv:2401.16008