Half period theorem of binary black holes

TL;DR

This paper investigates the orbital behavior of event horizons in binary black holes, revealing they merge quickly and cannot orbit for half a period, unlike apparent horizons which can orbit multiple times.

Contribution

It introduces the half period theorem for event horizons, showing a fundamental difference in orbital duration compared to apparent horizons in binary black hole mergers.

Findings

Event horizons merge quickly, typically within less than half an orbit.

Apparent horizons can orbit multiple times before merging.

Event horizons do not sustain half-period orbits, unlike apparent horizons.

Abstract

Merging event horizons of the binary black holes is investigated. While recent development of the numerical study of the binary black hole coalescence has shown that their apparent horizons can orbit for many periods, we study the orbital motion of the event horizon. We discuss how many periods their event horizons orbit before their coalescence. Then, we find that they soon merge into one and the black holes cannot orbit for a half period while the apparent horizons can orbit many times.