Global versus Local Aspects of Critical Collapse

TL;DR

This thesis explores critical gravitational collapse of a scalar field, demonstrating that self-similarity and critical exponents can be observed both locally and globally, with implications for astrophysical observations and quasinormal mode behavior.

Contribution

It introduces a method to extract critical exponents from both local and global perspectives, linking self-similarity to observable signals at null infinity and analyzing quasinormal modes in near-critical evolutions.

Findings

Critical exponent can be extracted locally and globally.

Agreement of tail exponents with analytical predictions.

Correlation between radiation signals and quasinormal modes.

Abstract

This thesis deals with critical collapse of a massless scalar field coupled to Einstein's equations in spherical symmetry. The system is numerically investigated from both global and local points of view using a characteristic slicing and radial compactification. We find that the critical exponent that characterizes the discretely self-similar solution can be extracted both locally, in the self-similar region and globally, e.g. from the news function. In this sense, self-similarity is observable from future null infinity. For subcritical evolutions we have numerically analyzed the exponents of power-law tails and have found agreement with analytical calculations for radiation along null infinity and along timelike lines. We argue that for astrophysical observers the relevant falloff rate is that of future null infinity. We have also investigated the behavior of quasinormal modes (QNM) in near-critical evolutions. Although the perturbation theory underlying QNMs requires a fixed black hole background, we have found a surprising correlation between the radiation signal with the period of the first QNM determined by the time-dependent Bondi mass. In this context, we have also been able to verify a stationarity criterion based on QNMs for the Vaidya metric, which models the time-dependent Schwarzschild background.