Critical gravitational collapse of a non-minimally coupled scalar field

TL;DR

This study investigates the critical collapse of a non-minimally coupled scalar field, achieving high-precision measurements of critical parameters and revealing how strong coupling alters the collapse dynamics and echoing behavior.

Contribution

It provides highly accurate critical amplitude and exponent values for non-minimal coupling, introduces a shock-avoiding slicing condition for strong coupling simulations, and explores the impact of coupling strength on collapse dynamics.

Findings

Critical amplitude determined with precision of 10^{-12}

Critical and echoing exponents decrease with stronger coupling

Echoing behavior becomes more complex at high coupling

Abstract

We study the critical gravitational collapse of a massless scalar field non-minimally coupled to gravity, using a quadratic coupling function with a strength parameter $\xi$. We concentrate on critical phenomena of type II, and determine with an accuracy of at least $10^{-12}$ the value of the critical amplitude for collapse to a black hole, as well as the values of the critical and echoing exponents. Obtaining such high accuracy in the critical amplitude requires us to do a coordinate radial transformation that effectively increases resolution near the central regions by a factor of at least $10^3$. As expected, we find that for the case of small coupling the critical behaviour is very similar to that of a minimally coupled scalar field. On the other hand, for high coupling the dynamics become so violent that we need to introduce a special slicing condition, known as the shock-avoiding slicing condition, in order to avoid gauge pathologies that would otherwise cause our simulations to fail. With this new gauge condition we are able to perform high accuracy simulations even in the strong coupling regime, where we find that the critical and echoing exponents become significantly smaller, and that the echoing behavior is richer and can not be modelled by a single harmonic.