Collapse to black holes in Brans-Dicke theory. II. Comparison with general relativity

We discuss a number of long-standing theoretical questions about collapse to black holes in the Brans-Dicke theory of gravitation. Using a new numerical code we show that Oppenheimer-Snyder collapse in this theory produces black holes that are identical to those of general relativity in final equilibrium, but are quite different from those of general relativity during dynamical evolution. We find that there are epochs during which the apparent horizon of such a black hole passes outside the event horizon, and that the surface area of the event horizon decreases with time. This behavior is possible because theorems which prove otherwise assume ${\mathit{R}}_{\mathit{a}\mathit{b}}$ ${\mathit{l}}^{\mathit{a}}$ ${\mathit{l}}^{\mathit{b}}$≥0 for all null vectors ${\mathit{l}}^{\mathit{a}}$. We show that dynamical spacetimes in Brans-Dicke theory can violate this inequality, even in vacuum, for any value of ω.