Introductory lectures on the Effective One Body formalism

The Effective One Body (EOB) formalism is an analytical approach which aims at providing an accurate description of the motion and radiation of coalescing binary black holes. We present a brief review of the basic elements of this approach.Comment: 22 pages, 3 figures, lectures given at the Second ICRANet Stueckelberg Workshop on Relativistic Field Theories (Pescara, Italy, September 3-8, 2007); to be published in the International Journal of Modern Physics

Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order

We compute the radiation reaction force on the orbital motion of compact binaries to the 3.5 post-Newtonian (3.5PN) approximation, i.e. one PN order beyond the dominant effect. The method is based on a direct PN iteration of the near-zone metric and equations of motion of an extended isolated system, using appropriate ``asymptotically matched'' flat-space-time retarded potentials. The formalism is subsequently applied to binary systems of point particles, with the help of the Hadamard self-field regularisation. Our result is the 3.5PN acceleration term in a general harmonic coordinate frame. Restricting the expression to the centre-of-mass frame, we find perfect agreement with the result derived in a class of coordinate systems by Iyer and Will using the energy and angular momentum balance equations.Comment: 28 pages, references added, to appear in Classical and Quantum Gravit