ID: gr-qc/0512111

Extended-body approach to the electromagnetic self-force in curved spacetime

December 20, 2005

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On the self-force in electrodynamics and implications for gravity

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We consider the motion of charged point particles on Minkowski spacetime. The questions of whether the self-force is finite and whether mass renormalisation is necessary are discussed within three theories: In the standard Maxwell vacuum theory, in the non-linear Born-Infeld theory and in the higher-order Bopp-Podolsky theory. In a final section we comment on possible implications for the theory of the self-force in gravity.

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Gravitational self-force in nonvacuum spacetimes

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The gravitational self-force has thus far been formulated in background spacetimes for which the metric is a solution to the Einstein field equations in vacuum. While this formulation is sufficient to describe the motion of a small object around a black hole, other applications require a more general formulation that allows for a nonvacuum background spacetime. We provide a foundation for such extensions, and carry out a concrete formulation of the gravitational self-force in...

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In this work we look for a geometric description of non-gravitational forces. The basic ideas are proposed studying the interaction between a punctual particle and an electromagnetic external field. For this purpose, we introduce the concept of proper space-time, that allow us to describe this interaction in a way analogous to the one that the general relativity theory does for gravitation. The field equations that define this geometry are similar to the Einstein's equations,...

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Abraham I. Harte, Peter Taylor, Éanna É. Flanagan
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The self-force problem---which asks how self-interaction affects a body's motion---has been poorly studied for spacetime dimensions $d \neq 4$. We remedy this for all $d \geq 3$ by nonperturbatively constructing momenta such that forces and torques acting on extended, self-interacting electromagnetic charges have the same functional forms as their test body counterparts. The electromagnetic field which appears in the resulting laws of motion is not however the physical one, b...

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Radiation reaction in curved space-time: local method

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Dmitri Gal'tsov, Pavel Spirin, Simona Staub
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Although consensus seems to exist about the validity of equations accounting for radiation reaction in curved space-time, their previous derivations were criticized recently as not fully satisfactory: some ambiguities were noticed in the procedure of integration of the field momentum over the tube surrounding the world-line. To avoid these problems we suggest a purely local derivation dealing with the field quantities defined only {\em on the world-line}. We consider point pa...

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The electromagnetic self-force of a Lorentz-contractible spherical shell of radius $R$ in rectilinear arbitrary motion: the terms of order $1/R$ and $R^0$

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G. Vaman
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We write the electromagnetic self-force of a Lorentz-contractible spherical shell of radius $R$ in arbitrary rectilinear motion as a series expansion in powers of $R$, and calculate the first two terms of this series. The method we use, which is based on the description of the particle in terms of a velocity-dependent volume charge density, avoids some important difficulties of the previous approaches from the literature. We compare our results with the results obtained by ot...

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Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge

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Celis Emilio Rubín de
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The electrostatic self-force on a point charge in cylindrical thin-shell space-times is interpreted as the sum of a $bulk$ field and a $shell$ field. The $bulk$ part corresponds to a field sourced by the test charge placed in a space-time without the shell. The $shell$ field accounts for the discontinuity of the extrinsic curvature ${\kappa^p}_q$. An equivalent electric problem is stated, in which the effect of the shell of matter on the field is reconstructed with the electr...

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Self-forces in arbitrary dimensions

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Abraham I. Harte, Peter Taylor, Éanna É. Flanagan
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Bodies coupled to electromagnetic or other long-range fields are subject to radiation reaction and other effects in which their own fields can influence their motion. Self-force phenomena such as these have been poorly understood for spacetime dimensions not equal to four, despite the relevance of differing dimensionalities for holographic duals, effectively two-dimensional condensed matter and fluid systems, and so on. We remedy this by showing that forces and torques acting...

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Radiation from a charged particle and radiation reaction -- revisited

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Abhinav Gupta, T. Padmanabhan
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We study the electromagnetic fields of an arbitrarily moving charged particle and the radiation reaction on the charged particle using a novel approach. We first show that the fields of an arbitrarily moving charged particle in an inertial frame can be related in a simple manner to the fields of a uniformly accelerated charged particle in its rest frame. Since the latter field is static and easily obtainable, it is possible to derive the fields of an arbitrarily moving charge...

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Electromagnetic self-force for axially symmetric charge on a spherical shell

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Andrew Steane
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We obtain the fields and electromagnetic self-force of a charge distributed on the surface of a sphere undergoing rigid motion at constant proper acceleration, where the charge distribution has axial symmetry about the direction of motion. A closed-form expression for the self-force is given in terms of the multipole moments of the charge distribution. Applications to the electrodynamics of a dipole, and to electromagnetic self-force near a horizon (in spacetime) are discusse...

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