New conformally flat initial data for spinning black holes

TL;DR

This paper introduces a new explicit solution for initial data of spinning black holes that reduces radiation and allows for higher rotation parameters, providing a better approximation to maximally rotating Kerr black holes.

Contribution

The authors present an explicit solution to the momentum constraint for spinning black holes that improves upon previous models by reducing radiation and enabling higher spin parameters.

Findings

Less radiation in initial data compared to Bowen-York solutions.

Higher maximum rotation parameter $J/m^2$ achievable.

Potential for more accurate modeling of near-extremal Kerr black holes.

Abstract

We obtain an explicit solution of the momentum constraint for conformally flat, maximal slicing, initial data which gives an alternative to the purely longitudinal extrinsic curvature of Bowen and York. The new solution is related, in a precise form, with the extrinsic curvature of a Kerr slice. We study these new initial data representing spinning black holes by numerically solving the Hamiltonian constraint. They have the following features: i) Contain less radiation, for all allowed values of the rotation parameter, than the corresponding single spinning Bowen-York black hole. ii) The maximum rotation parameter $J/m^2$ reached by this solution is higher than that of the purely longitudinal solution allowing thus to describe holes closer to a maximally rotating Kerr one. We discuss the physical interpretation of these properties and their relation with the weak cosmic censorship conjecture. Finally, we generalize the data for multiple black holes using the ``puncture'' and isometric formulations.