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Gravitational Self-Force: Orbital Mechanics Beyond Geodesic Motion

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General Relativity, Cosmology and Astrophysics

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 177))

Abstract

The question of motion in a gravitationally bound two-body system is a longstanding open problem of General Relativity. When the mass ratio \(\eta \) is small, the problem lends itself to a perturbative treatment, wherein corrections to the geodesic motion of the smaller object (due to radiation reaction, internal structure, etc.) are accounted for order by order in \(\eta \), using the language of an effective gravitational self-force. The prospect for observing gravitational waves from compact objects inspiralling into massive black holes in the foreseeable future has in the past 15 years motivated a program to obtain a rigorous formulation of the self-force and compute it for astrophysically interesting systems. I will give a brief survey of this activity and its achievements so far, and will identify the challenges that lie ahead. As concrete examples, I will discuss recent calculations of certain conservative post-geodesic effects of the self-force, including the \(O(\eta )\) correction to the precession rate of the periastron. I will highlight the way in which such calculations allow us to make a fruitful contact with other approaches to the two-body problem.

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Acknowledgments

This work was supported by the European Research Council under grant No. 304978; and by STFC in the UK through grant number PP/E001025/1.

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  1. School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK

    Leor Barack

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  1. Faculty of Mathematics and Physics, Charles University, Praha 8, Czech Republic

    Jiří Bičák

  2. Faculty of Mathematics and Physics, Charles University, Praha 8, Czech Republic

    Tomáš Ledvinka

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Barack, L. (2014). Gravitational Self-Force: Orbital Mechanics Beyond Geodesic Motion. In: Bičák, J., Ledvinka, T. (eds) General Relativity, Cosmology and Astrophysics. Fundamental Theories of Physics, vol 177. Springer, Cham. https://doi.org/10.1007/978-3-319-06349-2_6

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