A Pseudospectral Method for Gravitational Wave Collapse

TL;DR

This paper introduces 'bamps', a new pseudospectral numerical relativity code designed for simulating gravitational wave collapse, with specialized methods for axisymmetric data, horizon finding, and black hole formation.

Contribution

The paper develops a novel pseudospectral code with tailored boundary conditions, gauge treatments, and excision techniques for accurate simulation of gravitational collapse and black hole formation.

Findings

Successful evolution of Schwarzschild perturbed by gravitational waves

Demonstration of black hole formation from supercritical Brill waves

Strong-scaling performance of the pseudospectral code

Abstract

We present a new pseudospectral code, bamps, for numerical relativity written with the evolution of collapsing gravitational waves in mind. We employ the first order generalized harmonic gauge formulation. The relevant theory is reviewed and the numerical method is critically examined and specialized for the task at hand. In particular we investigate formulation parameters, gauge and constraint preserving boundary conditions well-suited to non-vanishing gauge source functions. Different types of axisymmetric twist-free moment of time symmetry gravitational wave initial data are discussed. A treatment of the axisymmetric apparent horizon condition is presented with careful attention to regularity on axis. Our apparent horizon finder is then evaluated in a number of test cases. Moving on to evolutions, we investigate modifications to the generalized harmonic gauge constraint damping scheme to improve conservation in the strong field regime. We demonstrate strong-scaling of our pseudospectral penalty code. We employ the Cartoon method to efficiently evolve axisymmetric data in our 3+1 dimensional code. We perform test evolutions of Schwarzschild perturbed by gravitational waves and by gauge pulses, both to demonstrate the use of our blackhole excision scheme and for comparison with earlier results. Finally numerical evolutions of supercritical Brill waves are presented to demonstrate durability of the excision scheme for the dynamical formation of a blackhole.