15th Capra Meeting on Radiation Reaction in General Relativity

Constructing a Hamiltonian for the Conservative Self-Force

Justin Vines

Cornell University

We suggest an approach towards computation of gravitational self-forces for bound orbits in Kerr which may have some advantages over previous approaches. The essential idea is to compute separately the dissipative and conservative pieces of the force. The dissipative piece, which drives the leading order inspiral, can be computed from the half-retarded minus half-advanced prescription, and does not require any regularization. We parameterize the dissipative piece in terms of its Fourier components on the torus in phase space, with respect to a Fourier decomposition using action-angle variables. We show that these Fourier components can be obtained from a fairly trivial generalization of existing frequency domain Teukolsky codes. The conservative piece can be parameterized in terms of a Hamiltonian on the phase space. We explore methods of constructing a regularized Hamiltonian, considering various levels of approximation. Taking care of regularization issues at the level of the Hamiltonian may provide calculational advantages over techniques that directly regularize the self-force. We will present preliminary numerical results relevant to these issues.