Oppenheimer-Snyder Collapse in Moving-Puncture Coordinates

TL;DR

This paper investigates how moving-puncture coordinates behave during the collapse of a dust sphere into a black hole, demonstrating their effectiveness in avoiding singularities even without pressure.

Contribution

It provides the first analytical and numerical analysis of moving-puncture coordinates in dust collapse scenarios, extending understanding beyond vacuum black holes.

Findings

Moving-puncture coordinates avoid singularities during dust collapse.

The geometry settles into a trumpet slice of a vacuum black hole.

Analytical expressions for density, lapse, and curvature at early times.

Abstract

Moving-puncture coordinates are commonly used in numerical simulations of black holes. Their properties for vacuum Schwarzschild black holes have been analyzed in a number of studies. The behavior of moving-puncture coordinates in spacetimes containing matter, however, is less well understood. In this paper we explore the behavior of these coordinates for Oppenheimer-Snyder collapse, i.e., the collapse of a uniform density, pressureless sphere of dust initially at rest to a black hole. Oppenheimer-Snyder collapse provides a stringent test of the singularity-avoiding properties of moving-puncture coordinates, since the singularity can form more quickly than it would for matter with pressure. Our results include analytical expressions for the matter density, lapse function, and mean curvature at early times, as well as interesting limits for later times. We also carry out numerical simulations to obtain the full solution and these show that, even in the absence of pressure, moving-puncture coordinates are able to avoid the singularity. At late times the geometry settles down to a trumpet slice of a vacuum black hole.