Black hole area in Brans-Dicke theory.

We have shown that the dynamics of the scalar field φ(x) = “G−1(x)” in BransDicke 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 non-decreasing 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 have been demonstrated for Oppenheimer-Snyder collapse in Brans-Dicke theory. PACS number(s): 04.70.-s, 04.70.Bw, 04.70.Dy