Numerical-relativity simulations of the quasi-circular inspiral and merger of non-spinning, charged black holes: methods and comparison with approximate approaches

TL;DR

This paper presents detailed numerical simulations of charged black hole mergers, introduces a formalism for electromagnetic wave analysis, compares results with approximate models, and discusses implications for gravitational wave detection of black hole charge.

Contribution

It introduces a formalism for electromagnetic wave analysis in black hole mergers and compares full simulations with approximate models, highlighting the accuracy of different approaches.

Findings

Newtonian quadrupole models have 20-100% errors in key quantities.

Test particle estimates of remnant spin agree within a few percent.

Electromagnetic contributions to black hole properties are quantified.

Abstract

We present fully general relativistic simulations of the quasi-circular inspiral and merger of charged, non-spinning, binary black holes with charge-to-mass ratio $\lambda \le 0.3$. We discuss the key features that enabled long term and stable evolutions of these binaries. We also present a formalism for computing the angular momentum carried away by electromagnetic waves, and the electromagnetic contribution to black-hole horizon properties. We implement our formalism and present the results for the first time in numerical-relativity simulations. In addition, we compare our full non-linear solutions with existing approximate models for the inspiral and ringdown phases. We show that Newtonian models based on the quadrupole approximation have errors of 20 % - 100 % in key gauge-invariant quantities. On the other hand, for the systems considered, we find that estimates of the remnant black hole spin based on the motion of test particles in Kerr-Newman spacetimes agree with our non-linear calculations to within a few percent. Finally, we discuss the prospects for detecting black hole charge by future gravitational-wave detectors using either the inspiral-merger-ringdown signal or the ringdown signal alone.