Abstract
While being as old as general relativity itself, the gravitational two-body problem has never been under so intense investigation as it is today, spurred by both phenomenological and theoretical motivations. The observations of gravitational waves emitted by compact binary coalescences bear the imprint of the source dynamics, and as the sensitivity of detectors improve over years, more accurate modeling is being required. The analytic modeling of classical gravitational dynamics has been enriched in this century by powerful methods borrowed from field theory. Despite being originally developed in the context of fundamental particle quantum scatterings, their applications to classical, bound system problems have shown that many features usually associated with quantum field theory, such as, e.g., divergences and counterterms, renormalization group, loop expansion, and Feynman diagrams, have only to do with field theory, be it quantum or classical. The aim of this work is to present an overview of this approach, which models massive astrophysical objects as nonrelativistic particles and their gravitational interactions via classical field theory, being well aware that while the introductory material in the present article is meant to represent a solid background for newcomers in the field, the results reviewed here will soon become obsolete, as this field is undergoing rapid development.
Highlights
The recent detections of gravitational waves (GWs) [1,2,3] by the large interferometric detectors LIGO [4] and Virgo [5] have revived the scientific interest on the gravitational two-body problem
The waveform templates used in the LIGO/Virgo data analysis pipeline [7] have been coded over decades building on several different approaches, relying both on the analytic and numerical knowledge of the source gravitational dynamics and on phenomenological methods to describe the spacetime deformation around them
Only longitudinal modes contribute to the conservative dynamics, a fact used in standard approach to PN approximation to decompose the contributions of the gravitational interactions into a near and a far zone, corresponding to the scale separation between the size of the binary system r and the gravitational wavelength λ ∼ T ∼ r/v r of emitted radiation, with T being the orbital period
Summary
The recent detections of gravitational waves (GWs) [1,2,3] by the large interferometric detectors LIGO [4] and Virgo [5] have revived the scientific interest on the gravitational two-body problem. All events detected so far have been originated by coalescences of compact binary systems, which are best searched for by correlating noisy observational data with precomputed waveform models, or templates, via standard matched-filtering [6]. The waveform templates used in the LIGO/Virgo data analysis pipeline [7] have been coded over decades building on several different approaches, relying both on the analytic and numerical knowledge of the source gravitational dynamics and on phenomenological methods to describe the spacetime deformation around them. One of the most successful perturbative analytic method has been the post-Newtonian (PN) approximation to GR, see [8] for a review, together with the self-force (SF) approach, see [9] for a recent review, whose small expansion parameter is the ratio of masses of the two objects composing the binary system. Building on results from all these approaches, two main families of accurate templates have been built: one using the effective one body framework [11], which mapped the two-body dynamics into that of a test body immersed in an effective Schwarzschildlike metric (see, e.g., [12] for the latest version), and the other leading to phenomenological waveforms
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