2005/01/13 by Eran Rosenthal
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Equations of motion #Gravitation #Gravitational wave #Mathematical physics #Nonlinear system #Perturbation (astronomy) #Physics #Point particle #Pulsars and Gravitational Waves Research #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Regularization (linguistics) #Scalar (mathematics) #Scalar field #Spacetime #gr-qc
paper · pdf · doi:10.1088/0264-9381/22/15/013
published as Class.Quant.Grav. 22 (2005) S859 · 14 pages
arxiv created 2005/01/13 · openalex publication_date 2005/07/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Accurate calculation of the motion of a compact object in a background spacetime induced by a supermassive black hole is required for the future detection of such binary systems by the gravitational-wave detector LISA. Reaching the desired accuracy requires calculation of the second-order gravitational perturbations produced by the compact object. At the point-particle limit the second-order gravitational perturbation equations turn out to have highly singular source terms, for which the standard retarded solutions diverge. Here we study a simplified scalar toy-model in which a point particle induces a nonlinear scalar field in a given curved spacetime. The corresponding second-order scalar perturbation equation in this model is found to have a similar singular source term, and therefore its standard retarded solutions diverge. We develop a regularization method for constructing well-defined causal solutions for this equation. Notably these solutions differ from the standard retarded solutions, which are ill defined in this case.