  Lindblad resonances have been suggested as an important mechanism for angular
momentum transport and heating in discs in binary black hole systems. We
present the basic equations for the torque and heating rate for relativistic
thin discs subjected to a perturbation. The Lindblad resonance torque is
written explicitly in terms of metric perturbations for an equatorial disc in a
general axisymmetric, time-stationary spacetime with a plane of symmetry. We
show that the resulting torque formula is gauge-invariant. Computations for the
Schwarzschild and Kerr spacetimes are presented in the companion paper.
