Anisotropic deformations in a class of projectivelyinvariant metricaffine theories of gravity
Abstract
Among the general class of metricaffine theories of gravity, there is a special class conformed by those endowed with a projective symmetry. Perhaps the simplest manner to realise this symmetry is by constructing the action in terms of the symmetric part of the Ricci tensor. In these theories, the connection can be solved algebraically in terms of a metric that relates to the spacetime metric by means of the socalled deformation matrix that is given in terms of the matter fields. In most phenomenological applications, this deformation matrix is assumed to inherit the symmetries of the matter sector so that in the presence of an isotropic energymomentum tensor, it respects isotropy. In this work we discuss this condition and, in particular, we show how the deformation matrix can be anisotropic even in the presence of isotropic sources due to the nonlinear nature of the equations. Remarkably, we find that EddingtoninspiredBornInfeld (EiBI) theories do not admit anisotropic deformations, but more general theories do. However, we find that the anisotropic branches of solutions are generally prone to a pathological physical behaviour.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 November 2020
 DOI:
 10.1088/13616382/abb923
 arXiv:
 arXiv:2006.07406
 Bibcode:
 2020CQGra..37v5013J
 Keywords:

 alternative theories of gravity;
 metricaffine gravity;
 anisotropic solutions;
 General Relativity and Quantum Cosmology
 EPrint:
 31 pages, 5 figures, 1 column