Asymptotics of gravitational collapse of scalar waves

Through a combination of analytic and numerical techniques, the formation of a black hole by a self-gravitating, spherically symmetric, massless scalar field is investigated. The evolution algorithm incorporates a Penrose compactification so that the Bondi mass, the news function, and other radiation zone limits can be obtained numerically. The late time behavior recently established by Christodoulou is confirmed and new asymptotic relations for late time and for large amplitude limits are derived. For example, it is shown, that the Bondi mass MB and the scalar monopole moment Q satisfy the asymptotic relation MB∼ π‖Q‖/√2 at high amplitudes. It is found that the scalar monopole moment decays exponentially during black hole formation in contrast to the perturbation theory result for a power law decay rate in an Oppenheimer–Snyder background. It is demonstrated that the Newman–Penrose constant for the scalar field is globally well defined and has significant effects.