Perturbations and Critical Behavior in the Self-Similar Gravitational Collapse of a Massless Scalar Field

TL;DR

This paper analyzes the perturbations of a self-similar gravitational collapse solution for a massless scalar field, deriving exact equations and revealing a continuous spectrum, with implications for critical behavior and mass scaling.

Contribution

It provides an exact derivation of perturbation equations and uncovers a continuous spectrum, advancing understanding of critical phenomena in scalar field collapse.

Findings

Perturbation spectrum is continuous, not discrete.

Mass-scaling exponent is calculated as 1.

Exact solutions for perturbation equations are obtained.

Abstract

This paper studies the perturbations of the continuously self-similar critical solution of the gravitational collapse of a massless scalar field (Roberts solution). The perturbation equations are derived and solved exactly. The perturbation spectrum is found to be not discrete, but occupying continuous region of the complex plane. The renormalization group calculation gives the value of the mass-scaling exponent equal to 1.