Abstract
I present an overview of the methods involved in the computation of the scalar, electromagnetic, and gravitational self-forces acting on a point particle moving in a curved spacetime. For simplicity, the focus here will be on the scalar self-force. The lecture follows closely my review article on this subject [E. Poisson, Living Rev. Relativ. 7 (2004), http://www.livingreviews.org/lrr-2004-6]. I begin with a review of geometrical elements (Synge’s world function, the parallel propagator). Next I introduce useful coordinate systems (Fermi normal coordinates and retarded light-cone coordinates) in a neighborhood of the particle’s world line. I then present the wave equation for a scalar field in curved spacetime and the equations of motion for a particle endowed with a scalar charge. The wave equation is solved by means of a Green’s function, and the self-force is constructed from the field gradient. Because the retarded field is singular on the world line, the self-force must involve a regularized version of the field gradient, and I describe how the regular piece of the self-field can be identified. In the penultimate section of the lecture I put the construction of the self-force on a sophisticated axiomatic basis, and in the concluding section I explain how one can do better by abandoning the dangerous fiction of a point particle.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
S. Detweiler, Class. Q. Grav. 22, S681 (2005)
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)
S.E. Gralla, R.M. Wald, Class. Q. Grav. 25, 205009 (2008)
A.I. Harte, Phys. Rev. D 73, 065006 (2006)
J.M. Hobbs, Ann. Phys. (N.Y.) 47, 141 (1968)
Y. Mino, M. Sasaki, T. Tanaka, Phys. Rev. D 55, 3457 (1997)
E. Poisson, Living Rev. Rel. 7, URL (cited on 11 August 2010): http://www.livingreviews.org/lrr-2004-6
T.C. Quinn, Phys. Rev. D 62, 064029 (2000)
T.C. Quinn, R.M. Wald, Phys. Rev. D 56, 3381 (1997)
H. Spohn, Dynamics of Charged Particles and Their Radiation Field (Cambridge University Press, Cambridge, 2008)
J.L. Synge, Relativity: the General Theory (North-Holland, Amsterdam, 1960)
K.S. Thorne, J.B. Hartle, Phys. Rev. D 31, 1815 (1985)
X.H. Zhang, Phys. Rev. D 34, 991 (1986)
Acknowledgements
I wish to thank the organizers of the school for their kind invitation to lecture; Orléans in the summer is a very nice place to be. I wish to thank the participants for many interesting discussions. And finally, I wish to thank Bernard Whiting for his patience. This work was supported by the Natural Sciences and Engineering Research Council of Canada.
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
Poisson, E. (2009). Constructing the 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_11
Download citation
DOI: https://doi.org/10.1007/978-90-481-3015-3_11
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)