  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.
