Merger rate distribution of primordial black hole binaries with electric charges

Abstract

We consider gravitational radiation and electromagnetic radiation from point mass binary with electric charges in a Keplerian orbit, and calculate the merger rate distribution of primordial black hole binaries with charges and a general mass function by taking into account gravitational torque and electromagnetic torque by the nearest primordial black hole. We apply the formalism to the extremal charged case and find that $\alpha =-(m_i+m_j{)}^2{\partial }^2\ln \mathcal{R}(m_i,m_j)/\partial m_i\partial m_j=12/11$, which is independent of the mass function.

Comments: V2, references added; V3, 2 figures, 10 pages, PRD version;