Regularization of the second-order gravitational perturbations produced by a compact object

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Abstract
The equations for the second-order gravitational perturbations produced by a compact object have highly singular source terms at the point particle limit. At this limit the standard retarded solutions to these equations are ill defined. Here we construct well defined and physically meaningful solutions to these equations. These solutions are important for practical calculations: the planned gravitational-wave detector LISA requires preparation of waveform templates for the expected gravitational waves. Construction of templates with desired accuracy for extreme mass-ratio binaries, in which a compact object inspirals towards a supermassive black hole, requires calculation of the second-order gravitational perturbations produced by the compact object.