Gravitational Wave Driven Inspirals of Binaries Connected by Cosmic Strings

Abstract

We consider gravitational waves from a pair of monopoles or black holes that are moving non-relativistically and are connected by a cosmic string. Shortly after the binary's formation, the connecting string straightens due the direct coupling of its motion to gravitational radiation. Afterwards, the motion of the binary can be well-approximated by a non-relativistic motion of its components that have an additional constant mutual attraction force due to the tension of the straight string that connects them. The orbit shrinks due to the gravitational radiation backreacting on the binary's components. We find that if the binary's semimajor axis $a\gg \sqrt{R_1 R_2/μ}$, its eccentricity grows on the inspiral's timescale; here $R_1$ and $R_2$ are the gravitational radii of the binary components, and $μ$ is the dimensionless tension of the string. When the eccentricity is high, it approaches unity super-exponentially. If the binary's components are monopole-antimonopole pair, this leads to the physical collision that would likely destroy the string and annihilate the monopoles when the semimajor axis is still many orders of magnitude greater than the string thickness. If the binary's components are black holes, then the eccentricity reaches its peak when $a\sim \sqrt{R_1 R_2/μ}$, and then decays according to the standard Peter's formula. The black-hole spins initially become locked to the orbital motion, but then lag behind as the inspiral proceeds. We estimate the string-tension-induced dimensionless spins just prior to the merger and find them to be $\simμ^{3/8}\ll 1$.