Measuring the black hole spin direction in 3D Cartesian numerical relativity simulations

Abstract

We show that the so-called flat-space rotational Killing vector method for measuring the Cartesian components of a black hole spin can be derived from the surface integral of Weinberg's pseudotensor over the apparent horizon surface when using Gaussian normal coordinates in the integration. Moreover, the integration of the pseudotensor in this gauge yields the Komar angular momentum integral in a foliation adapted to the axisymmetry of the spacetime. As a result, the method does not explicitly depend on the evolved lapse $\alpha$ and shift ${\beta }^i$ on the respective timeslice, as they are fixed to Gaussian normal coordinates, while leaving the coordinate labels of the spatial metric ${\gamma }_{ij}$ and the extrinsic curvature $K_{ij}$ unchanged. Such gauge fixing endows the method with coordinate invariance, which is not present in integral expressions using Weinberg's pseudotensor, as they normally rely on the explicit use of Cartesian coordinates.

References in corpus (2)

• Spin Flips and Precession in Black-Hole-Binary Mergers
• Introduction to dynamical horizons in numerical relativity

Cited by in corpus (5)

• Numerical relativity in spherical coordinates: A new dynamical spacetime and general relativistic MHD evolution framework for the Einstein Toolkit
• Numerical relativity in spherical coordinates with the Einstein Toolkit
• Numerical relativity simulations of thick accretion disks around tilted Kerr black holes
• On the dynamics of tilted black hole-torus systems
• Pseudotensor applied to Numerical Relativity in Calculating Global Quantities