The trumpet solution from spherical gravitational collapse with puncture gauges

TL;DR

This paper demonstrates that evolving a spherical star collapse with puncture gauges results in a stationary trumpet solution, closely matching the known wormhole slice, due to the Gamma-driver shift condition's effects.

Contribution

It shows that the stationary end-state of spherical collapse with puncture gauges aligns with the trumpet solution, highlighting the role of the Gamma-driver shift condition.

Findings

The end-state closely matches the trumpet solution.

The Gamma-driver shift condition enables matter to fall into unresolved regions.

Stationary coordinates of the trumpet are found outside the matter.

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.