PT Journal
AU Beltran Jimenez, J
   de Andres, D
   Delhom, A
TI Anisotropic deformations in a class of projectively-invariant metric-affine theories of gravity
SO Classical and Quantum Gravity
JI Class. Quantum Gravity
PY 2020
BP 225013
EP 25pp
VL 37
IS 22
DI 10.1088/1361-6382/abb923
LA English
DE alternative theories of gravity; metric-affine gravity; anisotropic solutions
AB Among the general class of metric-affine 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 so-called 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 energy-momentum 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 non-linear nature of the equations. Remarkably, we find that Eddington-inspired-Born-Infeld (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.
ER