Abstract. We review the present status of the null cone approach to numerical evolution being developed by the Pittsburgh group. We describe the simplicity of the underlying algorithm as it applies to the global description of general relativistic spacetimes. We also demonstrate its effectiveness in revealing asymptotic physical properties of black hole formation in the gravitational collapse of a scalar field.

INTRODUCTION

We report here on a powerful new approach for relating gravitational radiation to its matter sources based upon the null cone initial value problem (NCIVP), which has been developed at the University of Pittsburgh. We are grateful to the many graduate students and colleagues who have made important contributions: Joel Welling (Pittsburgh Supercomputing Center), Richard Isaacson (National Science Foundation), Paul Reilly, William Fette (Pennsylvania State University at McKeesport) and Philipos Papadopoulous.

As will be detailed, the NCIVP has several major advantages for numerical implementation, (i) There are no constraint equations. This eliminates need for the time consuming iterative methods needed to solve the elliptic constraint equations of the canonical formalism, (ii) No second time derivatives appear so that the number of basic variables is half the number for the Cauchy problem. In fact, the evolution equations reduce to one complex equation for one complex variable. The remaining metric variables (2 real and 1 complex) are obtained by a simple radial integration along the characteristics.