Trumpet solution from spherical gravitational collapse with puncture gauges

Abstract

We investigate the stationary end state obtained by evolving a collapsing spherical star with the gauges routinely adopted to study puncture black holes. We compare the end state of the collapse with the trumpet solution found in the evolution of a single wormhole slice and show that the two solutions closely agree. We demonstrate that the agreement is caused by the use of the Gamma-driver shift condition, which allows the matter to fall inwards into a region of spacetime that is not resolved by the numerical grid, and which simultaneously finds the stationary coordinates of the trumpet outside the matter.