Spherically Symmetric Gravitational Collapse of Perfect Fluids

TL;DR

This paper develops a new coordinate system for spherically symmetric gravitational collapse of perfect fluids using the 3+1 formalism, simplifying the analysis by unifying interior and exterior solutions in one coordinate patch.

Contribution

It introduces a novel approach to modeling gravitational collapse that eliminates complex matching procedures and provides a new coordinate system for Schwarzschild spacetime.

Findings

Unified interior and exterior solutions in one coordinate patch

Derived a new generalized Painleve-Gullstrand coordinate system

Simplified the analysis of spherically symmetric collapse

Abstract

Formulating a perfect fluid filled spherically symmetric metric utilizing the 3+1 formalism for general relativity, we show that the metric coefficients are completely determined by the mass-energy distribution, and its time rate of change on an initial spacelike hypersurface. Rather than specifying Schwarzschild coordinates for the exterior of the collapsing region, we let the interior dictate the form of the solution in the exterior, and thus both regions are found to be written in one coordinate patch. This not only alleviates the need for complicated matching schemes at the interface, but also finds a new coordinate system for the Schwarzschild spacetime expressed in generalized Painleve-Gullstrand coordinates.