GRAVITATIONAL COLLAPSE IN A SINGLE COORDINATE SYSTEM

We formulate the problem of a gravitationally collapsing body in terms of a single set of coordinates that are employed both in the vacuum region outside the body and inside the body where there is a zero pressure perfect fluid. The spatial coordinate R is the usual Schwarzschild radial coordinate, while the time coordinate t is measured by radially falling geodesic clocks. It is possible to follow the collapse of the body entirely on a single (R,t) space-time diagram. We give analytical expressions for the metrics in the interior and exterior regions which join smoothly and naturally at the-surface of the collapsing body. Other features such as apparent and event horizons are also described. (C) 1995 American Association of Physics Teachers.