Self-similar collapse of a scalar field in dilaton gravity and critical behaviour

TL;DR

This paper derives new analytical self-similar solutions for scalar field collapse in scalar-tensor theories, revealing critical behavior and calculating black hole mass scaling laws, which differ slightly from general relativity.

Contribution

It introduces novel analytical self-similar solutions for scalar field collapse in scalar-tensor theories and analyzes their critical behavior and black hole mass scaling laws.

Findings

Black hole mass scales as $M_{BH}=f(p-p_{cr})(p-p_{cr})^eta$ in some theories.

Critical exponent $eta$ is explicitly calculated.

Mass law differs from the general relativistic case.

Abstract

We present new analytical self-similar solutions describing a collapse of a massless scalar field in scalar-tensor theories. The solutions exhibit a type of critical behavior. The black hole mass for the near critical evolution is analytically obtained for several scalar-tensor theories and the critical exponent is calculated. Within the framework of the analytical models we consider it is found that the black hole mass law for some scalar-tensor theories is of the form $M_{BH}=f(p-p_{cr})(p-p_{cr})^\gamma$ which is slightly different from the general relativistic law $M_{BH}=const (p-p_{cr})^\gamma$.