Pseudospectral collocation methods for the computation of the self-force on a charged particle: Generic orbits around a Schwarzschild black hole

Priscilla Canizares, Carlos F. Sopuerta, José Luis Jaramillo

    Research output: Contribution to journalArticleResearchpeer-review

    31 Citations (Scopus)

    Abstract

    The inspiral of a stellar compact object into a massive black hole, an extreme-mass-ratio inspiral, is one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna. We expect to be able to detect and analyze many cycles of these slowly inspiraling systems, which makes them truly high-precision tools for gravitational-wave astronomy. To that end, the use of very precise theoretical waveform templates in the data analysis is required. To build them, we need to have a deep understanding of the gravitational backreaction mechanism responsible for the inspiral. The self-force approach describes the inspiral as the action of a local force that can be obtained from the regularization of the perturbations created by the stellar compact object on the massive black hole geometry. In this paper we extend a new time-domain technique for the computation of the self-force from the circular case to the case of eccentric orbits around a nonrotating black hole. The main idea behind our scheme is to use a multidomain framework in which the small compact object, described as a particle, is located at the interface between two subdomains. Then, the equations at each subdomain are homogeneous wave-type equations, without distributional sources. In this particle-without-particle formulation, the solution of the equations is smooth enough to provide good convergence properties for the numerical computations. This formulation is implemented by using a pseudospectral collocation method for the spatial discretization, combined with a Runge-Kutta algorithm for the time evolution. We present results from several simulations of eccentric orbits in the case of a scalar charged particle around a Schwarzschild black hole, an excellent test bed model for testing the techniques for self-force computations. In particular, we show the convergence of the method and its ability to resolve the field and its derivatives across the particle location. Finally, we provide numerical values of the self-force for different orbital parameters. © 2010 The American Physical Society.
    Original languageEnglish
    Article number044023
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume82
    Issue number4
    DOIs
    Publication statusPublished - 11 Aug 2010

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