Charged Binaries in Gravitational Tides

TL;DR

This paper investigates how gravitational tides affect charged black hole binaries, deriving explicit formulas for orbital shifts and revealing that charge influences tidal effects, especially near extremal limits.

Contribution

It constructs a model of gravitational tides on charged black hole binaries and analyzes the resulting orbital shifts, including the ISCO and light ring, in the extreme mass-ratio limit.

Findings

Tidal corrections decrease as black hole charge increases.

Finite tidal effects persist in the extremal charge limit.

Explicit functions for tidal shifts are derived.

Abstract

Next-generation low-frequency interferometers are expected to detect binary systems near supermassive black holes, where tidal effects can alter significantly the motion of the binary. This motivates a broader investigation of how external gravitational fields influence the dynamics of physical systems. In this work, we consider a charged black hole binary system subject to a gravitational tide. We first construct a stationary gravitational tide acting on a dyonic Reissner-Nordstr\"om black hole and, focusing on the extreme mass-ratio limit, we analyze the motion of a test particle. By calculating the secular Hamiltonian of the test particle, we obtain the ISCO and light ring tidal shifts in terms of explicit functions of the parameters of the binary. Our results show that tidal corrections are suppressed as the charge of the black hole increases, but they persist in the extremal limit yielding a finite contribution. This work paves the way towards studying tidal effects on other charged systems, such as topological stars.