TL;DR
This paper investigates how the scalar field in Brans-Dicke gravity causes black hole horizon areas to oscillate, explaining the failure of the area theorem and proposing a related non-decreasing entropy-like quantity.
Contribution
It demonstrates the oscillatory behavior of black hole horizon areas in Brans-Dicke theory and identifies a non-decreasing entropy-related quantity in stationary solutions.
Findings
Horizon area oscillates during black hole evolution.
The area theorem does not hold in Brans-Dicke theory.
A non-decreasing entropy-like quantity exists in stationary solutions.
Abstract
We have shown that the dynamics of the scalar field 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.
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