Dimensional regularization of local singularities in the 4th post-Newtonian two-point-mass Hamiltonian

The article delivers the only still unknown coefficient in the 4th post-Newtonian energy expression for binary point masses on circular orbits as function of orbital angular frequency. Apart from a single coefficient, which is known solely numerically, all the coefficients are given as exact numbers. The shown Hamiltonian is presented in the center-of-mass frame and out of its 57 coefficients 51 are given fully explicitly. Those coefficients are six coefficients more than previously achieved [Jaranowski/Sch"afer, Phys. Rev. D 86, 061503® (2012)]. The local divergences in the point-mass model are uniquely controlled by the method of dimensional regularization. As application, the last stable circular orbit is determined as function of the symmetric-mass-ratio parameter.