Abstract
The motion of a sufficiently small body in general relativity should be accurately described by a geodesic. However, there should be “gravitational self-force” corrections to geodesic motion, analogous to the “radiation reaction forces” that occur in electrodynamics. It is of considerable importance to be able to calculate these self-force corrections in order to be able to determine such effects as inspiral motion in the extreme mass ratio limit. However, severe difficulties arise if one attempts to consider point particles in the context of general relativity. This article describes these difficulties and how they have been dealt with.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The product of two distributions can be defined if the decay properties of their Fourier transforms are such that the Fourier convolution integral defining their product converges. This will be the case when the wavefront sets of the distributions satisfy an appropriate condition (see [8]).
- 2.
“Strings” – that is, objects with a distributional stress–energy tensor corresponding to a delta-function with support on a timelike surface of co-dimension two – are a borderline case; see [5].
- 3.
This follows immediately from “elliptic regularity,” since the difference between two Green’s functions satisfies the source free Laplace equation (4).
- 4.
This is not true in the Lorentzian case; the singular behavior of, for example, the retarded, advanced, and Feynman propagators are different from each other.
References
S. Detweiler, B.F. Whiting, Phys. Rev. D 67, 024025 (2003)
B.S. DeWitt, R.W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960)
P.A.M. Dirac, Proc. R. Soc. Lond. A 167, 148 (1938)
P.R. Garabedian, Partial Differential Equations (Wiley, New York, 1964)
D. Garfinkle, Class. Q. Grav. 16, 4101 (1999)
R. Geroch, J. Traschen, Phys. Rev. D 36, 1017 (1987)
S.E. Gralla, R.M. Wald, Class. Q. Grav. 25, 205009 (2008)
L. Hormander, The Analysis of Linear Partial Differential Operators, I (Springer, Berlin, 1985)
L. Hormander, The Analysis of Linear Partial Differential Operators, IV (Springer, Berlin, 1985)
W. Israel, Nuovo Cimento B 44, 1 (1966); Lettere alla Redazione, ibidem 48, 463 (1967)
Y. Mino, M. Sasaki, T. Tanaka, Phys. Rev. D 55, 3457 (1997)
A. Papapetrou, Proc. R. Soc. Lond. A 209, 248 (1951)
E. Poisson, Living Rev. Rel. 7, URL (cited on 23 December 2008): http://www.livingreviews.org/lrr-2004-6
T.C. Quinn, R.M. Wald, Phys. Rev. D 56, 3381 (1997)
Acknowledgements
This research was supported in part by NSF grant PHY04-56619 to the University of Chicago.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Wald, R.M. (2009). Introduction to Gravitational Self-Force. In: Blanchet, L., Spallicci, A., Whiting, B. (eds) Mass and Motion in General Relativity. Fundamental Theories of Physics, vol 162. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3015-3_8
Download citation
DOI: https://doi.org/10.1007/978-90-481-3015-3_8
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-3014-6
Online ISBN: 978-90-481-3015-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)