Boosted Kerr black holes in general relativity

TL;DR

This paper derives a new exact solution in general relativity describing a boosted Kerr black hole with arbitrary motion and rotation, revealing asymmetries in the ergosphere and horizons, relevant for astrophysical black holes and gravitational wave remnants.

Contribution

It introduces the most general boosted Kerr black hole solution with five parameters, extending previous models to include arbitrary boosts and directions, and analyzes its geometric and physical properties.

Findings

The solution describes a black hole with asymmetric ergosphere due to boost.

Horizons remain spherical with radii depending on mass and rotation.

The geometry models astrophysical black holes and gravitational wave remnants.

Abstract

A solution of Einstein's vacuum field equation is derived that describes a general boosted Kerr black hole relative to a Lorentz frame at future null infinity. The metric contains five independent parameters -- mass $m$, rotation $\omega$, boost parameter $v/c$ and the boost direction defined by $(n_1,n_2,n_3)$ satisfying $(n_1)^2+(n_2)^2+(n_3)^2=1$ -- and reduces to the Kerr black hole when the boost parameter is zero and $n_1=1$. The solution describes the most general configuration that an astrophysical black hole must have. The black hole rotates about the $z$-axis with angular momentum proportional to $m \omega$ and the geometry has just one Killing vector $\partial/\partial{u}$, where $u$ is the retarded time coordinate. The boost turns the ergosphere asymmetric, with dominant lobes in the direction opposite to the boost. The event and Cauchy horizons, defined for the case $\omega < m$, are specified respectively by the radii $r_{\pm}=m \pm \sqrt{m^2-\omega^2}$. The horizons are topologically spherical and the singularity has the topology of a circle on planes that are orthogonal to the boost direction. We argue that this black hole geometry is the natural set to describe the remnants of the recently observed gravitational wave events $GW150914$, $GW151226$, $GW170814$ and $GW170817$\cite{gw1,gw2,gw3,gw4}. In the conclusions we discuss possible astrophysical processes in the asymmetric ergosphere and the electromagnetic dynamical effects that may result from the rotating black hole moving at relativistic speeds together with the precession of the boost axis about the rotation axis of the black hole.