We show that the dynamics of the scalar field φ(x)=``G^-1(x)'' in Brans-Dicke theories of gravity makes the surface area of the black hole horizon oscillatory during its dynamical evolution. It explicitly explains why the area theorem does not hold in Brans-Dicke theory. However, we show that there exists a certain nondecreasing quantity defined on the event horizon which is proportional to the black hole entropy for the case of stationary solutions in Brans-Dicke theory. Some numerical simulations are demonstrated for Oppenheimer-Snyder collapse in Brans-Dicke theory.
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G. Kang (1996) studied this question.
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