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

Abstract

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 $d\to 3$. Some so far unpublished details of the dimensional-continuation computation of the 3rd post-Newtonian two-point-mass ADM Hamiltonian are presented.

To appear in "Proceedings of the 11th Marcel Grossmann Meeting on General Relativity", edited by H.Kleinert, R.T.Jantzen and R.Ruffini, World Scientific, Singapore, 2008

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