Critical Behavior in the Brans-Dicke Theory of Gravitation

TL;DR

This paper investigates critical gravitational collapse in Brans-Dicke theory, revealing how self-similarity and critical exponents depend on the parameter , through analytical and numerical solutions.

Contribution

It extends the understanding of critical phenomena in scalar-tensor gravitation theories by analyzing self-similarity and critical exponents in the Brans-Dicke framework.

Findings

Continuous self-similarity for  > -3/2 in Roberts's solution

Discrete self-similarity for  > -3/2 in Choptuik's solution

Critical exponent varies with , echoing parameter weakly dependent

Abstract

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 $\omega > -3/2$ 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 $\omega > -3/2$ that at the critical solution shows discrete self-similarity, however, the critical exponent depends strongly on $\omega$ while the echoing parameter weakly on it.