Gödel and Gödel-type solutions in the Palatini $f(R,T)$ gravity theory

Abstract

The Palatini $f(R,T)$ gravity theory is considered. The standard Einstein-Hilbert action is replaced by an arbitrary function of the Ricci scalar $R$ and of the trace $T$ of the energy-momentum tensor. In the Palatini approach, the Ricci scalar is a function of the metric and the connection. These two quantities, metric and connection, are taken as independents variables. Then, it is examined whether Palatini $f(R,T)$ gravity theory allows solutions in which lead to violation of causality. The Gödel and Gödel-type space-times are considered. In addition, a critical radius, which permits to examine limits for violation of causality, is calculated. It is shown that, for different matter contents, non-causal solutions can be avoided in this Palatini gravitational theory.

arXiv comment15 pages, accepted for publication in IJMPD

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Cited by in corpus (2)

• Gödel-type solutions in $f(R,T,R_{\mu \nu }{T}^{\mu \nu }$) gravity
• Gödel-type solutions in hybrid metric-Palatini gravity