Abstract
We present a study of the generalized second law of thermodynamics in the scope of the \(f(R,T)\) theory of gravity, with \(R\) and \(T\) representing the Ricci scalar and trace of the energy-momentum tensor, respectively. From the energy-momentum tensor equation for the \(f(R,T)=R+f(T)\) case, we calculate the form of the geometric entropy in such a theory. Then, the generalized second law of thermodynamics is quantified and some relations for its obedience in \(f(R,T)\) gravity are presented. Those relations depend on some cosmological quantities, as the Hubble and deceleration parameters, and also on the form of \(f(T)\).
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Notes
The violation of the first law of thermodynamics is not an exclusive \(f(R,T)\) gravity feature. Miao et al. (2011) have proved that it also does not hold in \(f(T)\) gravity, for instance, with \(T\) being the torsion scalar.
As we shall revisit later, this function is not indeed general or arbitrary, since it is submissive to some physical conditions.
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P.H.R.S. Moraes would like to thank Sao Paulo Research Foundation (FAPESP), grant 2015/08476-0, for financial support.
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Momeni, D., Moraes, P.H.R.S. & Myrzakulov, R. Generalized second law of thermodynamics in \(f(R,T)\) theory of gravity. Astrophys Space Sci 361, 228 (2016). https://doi.org/10.1007/s10509-016-2784-2
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DOI: https://doi.org/10.1007/s10509-016-2784-2