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 in the analysis of both analytical solution and numerical one. By conformally transforming the Roberts’s solution into the Brans-Dicke frame, we find for $\omega >-3\mathrm{/}2$ that a continuous self-similarity continues and that the critical exponent does depend on $\omega$. By conformally transforming the Choptuik’s solution into the Brans-Dicke frame, we find for $\omega >-3\mathrm{/}2$ that at the critical solution shows discrete self-similarity, however, the critical exponent depends strongly on $\omega$ while the echoing parameter weakly on it.