TY - JOUR

T1 - Eccentric self-forced inspirals into a rotating black hole

AU - Lynch, Philip

AU - van de Meent, Maarten

AU - Warburton, Niels

PY - 2022/7/21

Y1 - 2022/7/21

N2 - We develop the first model for extreme mass-ratio inspirals (EMRIs) into a rotating massive black hole driven by the gravitational self-force (GSF). Our model is based on an action angle formulation of the method of osculating geodesics for eccentric, equatorial (i.e., spin-aligned) motion in Kerr space-time. The forcing terms are provided by an efficient spectral interpolation of the first-order GSF in the outgoing radiation gauge. We apply a near-identity (averaging) transformation to eliminate all dependence of the orbital phases from the equations of motion, while maintaining all secular effects of the first-order GSF at post-adiabatic order. This implies that the model can be evolved without having to resolve all O(10(5)) orbit cycles of an EMRI, yielding an inspiral model that can be evaluated in less than a second for any mass-ratio. In the case of a non-rotating central black hole, we compare inspirals evolved using self-force data computed in the Lorenz and radiation gauges. We find that the two gauges generally produce differing inspirals with a deviation of comparable magnitude to the conservative self-force correction. This emphasizes the need for including the (currently unknown) dissipative second order self-force to obtain gauge independent, post-adiabatic waveforms.

AB - We develop the first model for extreme mass-ratio inspirals (EMRIs) into a rotating massive black hole driven by the gravitational self-force (GSF). Our model is based on an action angle formulation of the method of osculating geodesics for eccentric, equatorial (i.e., spin-aligned) motion in Kerr space-time. The forcing terms are provided by an efficient spectral interpolation of the first-order GSF in the outgoing radiation gauge. We apply a near-identity (averaging) transformation to eliminate all dependence of the orbital phases from the equations of motion, while maintaining all secular effects of the first-order GSF at post-adiabatic order. This implies that the model can be evolved without having to resolve all O(10(5)) orbit cycles of an EMRI, yielding an inspiral model that can be evaluated in less than a second for any mass-ratio. In the case of a non-rotating central black hole, we compare inspirals evolved using self-force data computed in the Lorenz and radiation gauges. We find that the two gauges generally produce differing inspirals with a deviation of comparable magnitude to the conservative self-force correction. This emphasizes the need for including the (currently unknown) dissipative second order self-force to obtain gauge independent, post-adiabatic waveforms.

KW - extreme mass ratio inspirals

KW - gravitational self force

KW - relativistic celestial mechanics

KW - gravitational waveform modeling

KW - eccentricity

KW - GRAVITATIONAL-RADIATION REACTION

KW - TEUKOLSKY EQUATION

KW - ANALYTIC SOLUTIONS

KW - PERTURBATIONS

KW - WAVES

U2 - 10.1088/1361-6382/ac7507

DO - 10.1088/1361-6382/ac7507

M3 - Journal article

VL - 39

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 14

M1 - 145004

ER -