  We present a fully relativistic computation of the torques due to Lindblad
resonances from perturbers on circular, equatorial orbits on discs around
Schwarzschild and Kerr black holes. The computation proceeds by establishing a
relation between the Lindblad torques and the gravitational waveforms emitted
by the perturber and a test particle in a slightly eccentric orbit at the
radius of the Lindblad resonance. We show that our result reduces to the usual
formula when taking the nonrelativistic limit. Discs around a black hole
possess an m=1 inner Lindblad resonance with no Newtonian Keplerian analogue;
however its strength is very weak even in the moderately relativistic regime
(r/M ~ few tens), which is in part due to the partial cancellation of the two
leading contributions to the resonant amplitude (the gravitoelectric octupole
and gravitomagnetic quadrupole). For equatorial orbits around Kerr black holes,
we find that the m=1 ILR strength is enhanced for retrograde spins and
suppressed for prograde spins. We also find that the torque associated with the
m>=2 inner Lindblad resonances is enhanced relative to the nonrelativistic
case; the enhancement is a factor of 2 for the Schwarzschild hole even when the
perturber is at a radius of 25M.
