Lindblad resonance torques in relativistic discs: I. Basic equations

TL;DR

This paper derives the fundamental equations for Lindblad resonance torques and heating rates in relativistic thin discs around black holes, providing a gauge-invariant framework applicable to various spacetimes.

Contribution

It introduces a general, gauge-invariant formula for Lindblad resonance torques in relativistic discs, applicable to axisymmetric, stationary spacetimes.

Findings

Explicit torque formula in terms of metric perturbations

Gauge invariance of the resonance torque expression

Application framework for Schwarzschild and Kerr spacetimes

Abstract

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.