Half period theorem of binary black holes

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.