Seminarium Teorii Względności i Grawitacji

Recent applications of the ADM canonical formalism to the relativistic two-body problem will be presented. They concern derivation of the conservative equations of motion of compact binary systems up to at least 4th post-Newtonian (4PN) approximation of general relativity. The derivation employs Dirac delta distributions to model the compact bodies,what leads to ultra-violet divergencies which are regularized by a combination of Riesz-implemented Hadamard's partie finie approach and dimensional regularization. The infra-red ambiguity which plagues the derivation of the near-zone part of 4PN-accurate dynamics is resolved by taking into account the 4PN breakdown of the usual near-zone expansiondue to tail-transported nonlocal-in-time interaction between the bodies.The achieved results play a crucial role in the successful detections, by LIGO/Virgo detectors, of gravitational-wave signals coming from coalescing compact binaries, and for the estimation of the signals' parameters. [zoom for link ask: wkaminsk at fuw.edu.pl]