Dimensional regularization of the gravitational interaction of point masses in the ADM formalism

Details Dimensional regularization of the gravitational interaction of point masses in the ADM formalism Dimensional regularization of the gravitational interaction of point masses in the ADM formalism

2008-04-15

arxiv.org/abs/0804.2386v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

To appear in "Proceedings of the 11th Marcel Grossmann Meeting on General Relativity", edited by H.Kleinert, R.T.Jantzen and R

Scientific paper

The ADM formalism for two-point-mass systems in $d$ space dimensions is sketched. It is pointed out that the regularization ambiguities of the 3rd post-Newtonian ADM Hamiltonian considered directly in $d=3$ space dimensions can be cured by dimensional continuation (to complex $d$'s), which leads to a finite and unique Hamiltonian as $d\to3$. Some so far unpublished details of the dimensional-continuation computation of the 3rd post-Newtonian two-point-mass ADM Hamiltonian are presented.

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