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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., Comment: 23 pages, 4 figures

Binary-black-hole (BBH) mergers can take place close to a supermassive black hole (SMBH) while being in a bound orbit around the SMBH. In this paper, we study such bound triple systems and show that including the strong gravity effects of describing the SMBH with a Kerr metric can significantly modify the dynamics, as compared to a Newtonian point particle description of the SMBH. We extract the dynamics of the system, using a quadrupole approximation to the tidal forces due to the SMBH. We exhibit how the gyroscope precession is built into this dynamics, and find the secular Hamiltonian by both averaging over the inner and outer orbits, the latter being the orbit of the BBH around the SMBH. We study the long-time-scale dynamics, including the periastron precession and GW radiation-reaction of the binary system, finding that the strong gravity effects of the SMBH can enhance the von Zeipel-Lidov-Kozai mechanism, resulting in more cycles, higher maximum eccentricity, and thereby a shorter merger time, particularly when the binary is close to, or at, the innermost stable orbit of the SMBH. We end with an analysis of the peak frequency of the GW emission from the binary system, highlighting possible observable signatures in the LISA and ET frequency bands., Comment: 22 pages, 14 figures; V2 matched published version in MNRAS

The dynamics of a binary system moving in the background of a black hole is affected by tidal forces. In this work, for the Kerr black hole, we derive the electric and magnetic tidal moments at quadrupole order, where the latter are computed for the first time in full generality. We make use of these moments in the scenario of a hierarchical triple system made of a Kerr black hole and an extreme-mass ratio binary system consisting of a Schwarzschild black hole and a test particle. We study how the secular dynamics of the test particle in the binary system is distorted by the presence of tidal forces from a much larger Kerr black hole. Our treatment includes strong gravitational effects beyond the post-Newtonian approximation both for the binary system and for the tidal forces since the binary system is allowed to be close to the event horizon of the Kerr black hole. We compute the shifts in the physical quantities for the secular dynamics of the test particle and show that they are gauge-invariant. In particular, we apply our formalism to the innermost stable circular orbit for the test particle and to the case of the photon sphere. Our results are relevant for the astrophysical situation in which the binary system is in the vicinity of a supermassive black hole., Comment: v1: 27 pages, 3 figures; v2: minor changes, matches published version in Phys. Rev. D