We have shown 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 {\it 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.Comment: 12 pages, latex, 5 figures, epsfig.sty, some statements clarified and
two references added, to appear in Phys. Rev.
