Self-force: Computational Strategies
Building on substantial foundational progress in understanding the effect of a small body’s self-field on its own motion, the past 15 years has seen the emergence of several strategies for explicitly computing self-field corrections to the equations of mo
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Abstract Building on substantial foundational progress in understanding the effect of a small body’s self-field on its own motion, the past 15 years has seen the emergence of several strategies for explicitly computing self-field corrections to the equations of motion of a small, point-like charge. These approaches broadly fall into three categories: (i) mode-sum regularization, (ii) effective source approaches and (iii) worldline convolution methods. This paper reviews the various approaches and gives details of how each one is implemented in practice, highlighting some of the key features in each case.
1 Introduction Compact-object binaries are amongst the most compelling sources of gravitational waves. In particular, the ubiquity of supermassive black holes residing in galactic centres [1] has made the extreme mass ratio regime a prime target for the eLISA mission [2–6]. Meanwhile, the comparable and intermediate mass ratio regimes are an intriguing target for study by the imminent Advanced LIGO detector [7]. In order to maximise the scientific gain realised from gravitational-wave observations, highly accurate models of gravitational-wave sources are essential. For the case of extreme mass ratio inspirals (EMRIs)—binary systems in which a compact, solar mass object inspirals into an approximately million solar mass black hole—the demands of gravitational wave astronomy are particularly stringent; the promise of groundbreaking scientific advances—including precision tests of general relativity in the strong-field regime [8–10] and a better census of black hole populations—hinges on our ability to track the phase of their gravitational waveforms throughout the long inspiral, with an accuracy of better than 1 part in 10,000 [2]. This, in turn requires highly accurate, long time models of the orbital motion.
B. Wardell (B) Department of Astronomy, Cornell University, Ithaca, NY 14853, USA e-mail: [email protected] URL: http://www.barrywardell.net © Springer International Publishing Switzerland 2015 D. Puetzfeld et al. (eds.), Equations of Motion in Relativistic Gravity, Fundamental Theories of Physics 179, DOI 10.1007/978-3-319-18335-0_14
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For the past two decades, these demands have stimulated an intense period of EMRI research among the gravitational physics community. Despite of the impressive progress made by numerical relativists towards tackling the two-body problem in general relativity (for reviews see Refs. [11–13]), the disparity of length scales characterising the EMRI regime is a significant roadblock for existing numerical relativity techniques. Indeed, to this day EMRIs remain intractable by current numerical relativity methods, and successful approaches have instead tackled the problem perturbatively or through post-Newtonian approximations (see Ref. [14] for a review). This article will focus on the first of these; by treating the smaller object as a perturbation to the larger mass, the so-called “self-force approach” reviewed here has been a resoundingly successful to
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