Angular velocity of rotating black holes -- a new way to construct initial data for binary black holes

Abstract

Motivated by a geometric understanding of the angular velocity of a Kerr black hole in terms of a quasi-conformal map that describes a 2d Beltrami fluid flow, a new way to construct initial data sets for binary rotating black holes by prescribing the angular velocities of the two black holes at their horizons is discussed. A set of elliptic equations with prescribed Dirichlet boundary conditions at the horizons and at spatial infinity is established for constructing the initial data. To explore the dynamics encoded in these initial data, we consider the conformally flat three-metric case and numerically evolve it using the BSSN code for two co-rotating and counter-rotating black holes with angular velocities prescribed at the horizons. When the angular velocities are non-uniform and deviate from a constant value at the horizons, new gravitational waveforms are generated which display certain oscillatory pattern reminiscent of that of quasi-normal ringing in the inspiral phase before merger takes place.