  Astrophysical phenomena involving massive black holes (BHs) in close binaries
are expected to leave detectable signatures in the electromagnetic and
gravitational-wave spectrum. Such imprints may provide precious information to
probe the space-time around rotating BHs and to reveal new insights on the
nature of gravity in the strong-field regime. To support this observational
window, it is crucial to develop suitable tests to verify the predictions of
General Relativity. In this framework, the metric recently proposed by
Johannsen and Psaltis parametrizes strong-field deviations from a Kerr
space-time in a theory-independent way. In the following, we make use of this
approach to describe the tidal field produced by spinning BHs. We compute the
gravito-magnetic and gravito-electric tidal tensors for particles moving on
equatorial circular geodesics, comparing our results with those obtained in the
standard General Relativity scenario. Our calculations show significant
differences even for distances far form the last stable orbit, which may affect
the evolution of the binary and leave detectable signatures. We test our
framework computing quasiequilibrium sequences of BH-white dwarf systems by
means of the affine model, for different binary configurations.
