Extreme-mass-ratio inspirals in relativistic accretion discs

We compute relativistic Lindblad torques for circular, equatorial extreme-mass-ratio inspirals (EMRIs) embedded in relativistic thin accretion discs, including spinning black hole configurations. We find that relativistic effects can amplify the magnitude of these torques by orders of magnitude in the strong-field regime, and that the torque can even reverse direction as the EMRI approaches the innermost stable circular orbit (ISCO). However, we show that the location of this reversal is highly spin-dependent, shifting progressively closer to the ISCO, where gravitational-wave emission completely dominates the inspiral, as the spin of the central black hole increases. Spin also modifies the radial dependence of the Lindblad torques. We investigate whether Lindblad torques can be approximated by parametrized power laws of the form T LR = A ( r s / 10 M ) n r (or combinations thereof), and find significant spin- and disc-dependent variations in the slope parameter n r . For instance, for spin a / M = 0.9 , we find n r = 3.6 in the strong-field regime, compared to the Newtonian value of n r = 4.5 . Given current forecasts of parameter recovery for “golden,” loud EMRIs in accretion discs ( Δ n r ∼ 0.5 ), we predict LISA could distinguish between different disc configurations through their relativistic Lindblad torque signatures, providing the first direct probe of the midplane structure of the inner region of accretion discs, which is inaccessible to electromagnetic observations.