General Boosted Black Holes: A First Approximation

TL;DR

This paper presents an approximate solution to Einstein's equations describing a boosted Kerr-Newman black hole, incorporating effects of Lorentz boosts from the BMS group, and analyzes its spacetime structure and electromagnetic fields.

Contribution

It introduces a novel approximate metric for a boosted Kerr-Newman black hole derived from twisting metrics and explores its geometric and electromagnetic properties.

Findings

Solution satisfies Einstein equations up to fourth-order in 1/r

Event horizon and ergosphere are characterized in Bondi-Sachs coordinates

Electric field is purely radial while magnetic field has lobes opposite to boost direction

Abstract

In this paper we obtain an approximate solution of Einstein field equations which describes a general boosted Kerr-Newman black hole relative to a Lorentz frame at future null infinity. The boosted black hole is obtained from a general twisting metric whose boost emerges from the BMS group. Employing a standard procedure we build the electromagnetic energy-momentum tensor with the Kerr boosted metric together with its timelike Killing vector as the electromagnetic potential. We demonstrate that our solution satisfies Einstein field equations up to a fourth-order expansion in $1/r$, indicating that the spacetime closely resembles a Kerr-Newman black hole whose boost points in a arbitrary direction. Spacetime structures of the general black hole -- namely the event horizon and ergosphere -- are examined in Bondi-Sachs coordinates. For a proper timelike observer we show that the electric field generated by the boosted black hole exhibits a purely radial behavior, whereas the magnetic field develops a complex structure characterized by two pronounced lobes oriented opposite to the boost direction.