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General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
Abstract:
We implement the effective field theory for gravitating spinning objects in
the post-Newtonian scheme at the next-to-next-to-leading order level to derive
the gravitational spin-orbit interaction potential at the third and a half
post-Newtonian order for rapidly rotating compact objects. From the
next-to-next-to-leading order interaction potential, which we obtain here in a
Lagrangian form for the first time, we derive straightforwardly the
corresponding Hamiltonian. The spin-orbit sector constitutes the most elaborate
spin dependent sector at each order, and accordingly we encounter a
proliferation of the relevant Feynman diagrams, and a significant increase of
the computational complexity. We present in detail the evaluation of the
interaction potential, going over all contributing Feynman diagrams. The
computation is carried out in terms of the nonrelativistic gravitational
fields, which are advantageous also in spin dependent sectors, together with
the various gauge choices included in the effective field theory for
gravitating spinning objects, which also optimize the calculation. In addition,
we automatize the effective field theory computations, and carry out the
automated computations in parallel. Such automated effective field theory
computations would be most useful to obtain higher order post-Newtonian
corrections. We compare our Hamiltonian to the ADM Hamiltonian, and arrive at a
complete agreement between the ADM and effective field theory results. The
derivation presented here is essential to obtain further higher order
post-Newtonian corrections, and to reach the accuracy level required for the
successful detection of gravitational radiation.
