Abstrakt
We model the inspiral as taking place in the field of a Schwarzschild black hole perturbed by the gravitational field of a far axisymmetric distribution of mass enclosing the system. We take into account the redshift, frame-dragging, and quadrupolar tide caused by the enclosing matter, thus incorporating all effects to inverse third order of the characteristic distance of the enclosing mass.
Then, we use canonical perturbation theory to obtain the action-angle coordinates and Hamiltonian for mildly eccentric precessing test-particle orbits in this background. Finally, we use this to efficiently compute mildly eccentric inspirals in this field and document their properties.
This work shows the advantages of canonical perturbation theory for the modeling EMRIs, especially in the cases when the background deviates from the standard black hole fields.