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.

Simulations of rotating neutron star collapse with the puncture gauge: End state and gravitational waveforms

“…The end state of a spherical gravitational collapse asymptotically approaches the same trumpet solution found in vacuum simulations [21]. The agreement of end states is again caused by the spatial gauge condition, which allows the matter to fall inwards into a region of spacetime that is not resolved by the numerical grid.…”

“…Puncture gauge conditions play a key role in the simulations of rotational collapse as they "automatically" handle the singularity formation and subsequent evolution [20,21]. Building on previous work and extending it, we have demonstrated that the end state of an axisymmetric collapse in the puncture gauge is the same as the one obtained from the evolution of a spinning puncture [22].…”

“…An apparent horizon is first found at t ∼ 188M ⊙ (for resolution G11H). Soon after horizon formation, all the matter is inside the horizon and actually "falls off" the grid due to gauge conditions (see [21] and below). In Sec.…”

“…The agreement of end states is again caused by the spatial gauge condition, which allows the matter to fall inwards into a region of spacetime that is not resolved by the numerical grid. As stressed in [21], the result is nontrivial because in the collapsing spacetime there is (at least in the matter region) no timelike Killing vector that can lead to a stationary end state, and, at the continuum level, it has different topology than the puncture. Trumpet solutions are also found in dust and gravitational wave collapse [46,47].…”

General-relativistic resistive magnetohydrodynamics in three dimensions: Formulation and tests

“…While the left panel of Fig. 13 shows that most of the rest-mass is dissipated away already by t = 0.65 ms (see discussion in [69] about why this happens), some of the matter remains on the grid near the singularity, anchoring there the magnetic field which slowly evolves as shown in the middle and right panels. A complementary view of the collapse process is also offered by Fig.…”