Brans-Dicke theory and thermodynamical laws on apparent and event horizons

摘要

In this work, we describe the Brans–Dicke (BD) theory of gravity and give a particular solution by choosing anpower law form for the scalar field f and constant u. If we assume that the first law of thermodynamics and the entropy formulanhold on the apparent horizon, then we recover the Friedmann equations. Next, assuming the first law of thermodynamicsnholds, the validity conditions of the generalized second law (GSL) on the event horizon are presented. If we impose thenentropy relation on the horizon, without using the first law, then we also obtain the validity condition of the GSL on thenevent horizon. The validity of the GSL completely depends on the BD model scalar field solutions. We have justified thatnthe two processes are equivalent on the apparent horizon, but on the event horizon they are not equivalent. If the first law isnvalid on the event horizon, then the GSL may be satisfied by the BD solution, but if the first law is not satisfied then thenGSL is not satisfied by the BD solution. Therefore, the first law always favours the GSL on the event horizon. In our effectivenapproach, the first law and the GSL are always satisfied on the apparent horizon, which does not depend on the BDntheory of gravity.