Critical Behavior in the Brans-Dicke Theory of Gravitation

The collapse of a massless scalar field in the Brans-Dicke theory of gravitation is studied both under self-similar symmetry and under asymptotic flat boundary conditions. In the self-similar case, we find the critical exponent depends on ω, namely . In the case of the asymptotic flat space-time, we use numerical method and find that the critical solution shows discrete self-similarity and that the critical exponent depends on ω, while the echoing parameter depends weakly on it.