Dustball collapse and evaporation in standard coordinates

Abstract

We consider evaporation alongside collapse for a dustball in standard (not comoving) coordinates. A classical analysis gives the main result: an explicit metric (joined to the exterior) for the collapse. The metric then provides the causal structure: light cones corresponding to the coordinate speed of light, c. If the problem is perturbed from a pure dustball collapse, the solution can only be altered within the future light cones of such perturbations. The metric tells us that c_{interior} << c_{exterior}. Importantly, the speed at which the Schwarzschild radius shrinks during evaporation is intermediate between the two. Thus a perturbation at the (shrinking) surface will only influence the exterior in finite time. For example, if we assume evaporation to be a process located at the dustball's surface, we can model it as a series of perturbations to the classical solution. In this modified solution, the interior is not altered as the evaporation process eats into a frozen interior from the outside in; the singularity and a region near it are no longer present; infalling particles don't cross the (shrinking) dustball boundary; the metric coefficients don't change sign with time, and therefore timelike world lines can exist at constant radius inside the (shrinking) Schwarzschild radius and emerge at late times (no absolute horizon forms). Research on evaporation alongside collapse typically study collapsing shells and apply quantum field theory. This paper differs in that it studies an entire dustball and uses classical general relativity to constrain evaporation models.