Abstract. The results of a detailed numerical investigation of the strong-field, dynamical behaviour of a collapsing massless scalar field coupled to the gravitational field in spherical symmetry are summarized. A variety of non-linear phenomena suggestive of a type of universality in the model have been discovered using a finite difference approach combined with an adaptive mesh algorithm based on work by Berger & Oliger. A derivation of the equations of motion for the system is sketched, the adaptive algorithm is described, and representative examples of the strong-field behaviour are displayed.

INTRODUCTION

The problem of the collapse of a massless scalar field coupled to the Einstein gravitational field in spherical symmetry has been studied in considerable detail, both analytically (Christodoulou 1986a, 1986b, 1987a, 1987b), and through numerical work (Choptuik 1986, 1989, 1991, Goldwirth & Piran 1987, Goldwirth et al 1989, Gómez & Winicour 1989, 1992, Gómez et al 1992). In many ways, the system provides an ideal model for addressing a variety of basic issues in numerical relativity. The scalar field provides the model with a radiative degree of freedom which is necessarily absent from any “dynamics” of the Einstein (or Maxwell) field in spherical symmetry. At the same time, by suitable choice of initial data, the self-gravitation of the scalar field can be made arbitrarily strong, so that processes such as curvature scattering of radiation and black-hole formation can be studied.