A spherical black hole gauge transformation for modeling rapidly spinning black holes with SpECTRE

SpECTRE is a new numerical-relativity code (currently under development) that will calculate the gravitational waves emitted by colliding black holes with unprecedented accuracy, which will help scientists interpret observations from next-generation gravitational-wave detectors. It can achieve high accuracy in part through using novel techniques to scale to hundreds of thousands of compute cores—far more than typical numerical-relativity codes can efficiently use.  Modeling rapidly spinning binary black holes with high accuracy is especially challenging, in part because. the conventional description of a rotating black hole uses coordinates in which the horizon (surface of the black hole) is oblate. I will discuss the implementation in SpECTRE of the coordinate transformation recently proposed by Chen, Deppe, Kidder, and Teukolsky (doi:10.1103/PhysRevD.104.084046) that ensures that the horizon is spherical, even when the black hole is spinning nearly as rapidly as possible. These coordinates are better adapted to the underlying symmetry; using them requires fewer grid points to simulate rapidly spinning black-hole spacetimes accurately.