Challenging the Paradigm of Singularity Excision in Gravitational Collapse

A paradigm deeply rooted in modern numerical relativity calculations prescribes the removal of those regions of the computational domain where a physical singularity may develop. We here challenge this paradigm by performing three-dimensional simulations of the collapse of uniformly rotating stars to black holes without excision. We show that this choice, combined with suitable gauge conditions and the use of minute numerical dissipation, improves dramatically the long-term stability of the evolutions. In turn, this allows for the calculation of the waveforms well beyond what was previously possible, providing information on the black-hole ringing and setting a new mark on the present knowledge of the gravitational-wave emission from the stellar collapse to a rotating black hole.

Figure 1

Evolution of the normalized maximum of the rest-mass density ${\rho }_{\max }$ (solid line) and of the total rest-mass $M_{*}$ (dashed line) for model D4. Circles indicate the times at which the AH is first found and thick lines the results obtained with excision.

Figure 2

Evolution of the $L2$ norm of the Hamiltonian-constraint violation for model D1. Different curves refer to the violation computed only inside the AH (short-dashed line), only outside it (continuous line) or when the excision is made (long-dashed line in the inset). The circles show the rescaled violation for a higher resolution.

Figure 3

Lowest gauge-invariant multipole for a slowly rotating star (left panel) and a rapidly rotating one (right panel). Thick lines refer to evolutions carried out with excision and terminate at a code crash, while the circles indicate the AH formation time.