# Rigorous derivation of electromagnetic self-force

@article{Gralla2009RigorousDO, title={Rigorous derivation of electromagnetic self-force}, author={Samuel E. Gralla and Abraham I. Harte and Robert M. Wald}, journal={Physical Review D}, year={2009}, volume={80}, pages={024031} }

During the past century, there has been considerable discussion and analysis of the motion of a point charge in an external electromagnetic field in special relativity, taking into account 'self-force' effects due to the particle's own electromagnetic field. We analyze the issue of 'particle motion' in classical electromagnetism in a rigorous and systematic way by considering a one-parameter family of solutions to the coupled Maxwell and matter equations corresponding to having a body whose…

## 109 Citations

### Force on a point charge source of the classical electromagnetic field

- PhysicsPhysical Review D
- 2019

It is shown that a well-defined expression for the total electromagnetic force $f^{em}$ on a point charge source of the classical electromagnetic field can be extracted from the postulate of total…

### Radiation-reaction force on a small charged body to second order

- Physics
- 2015

In classical electrodynamics, an accelerating charged body emits radiation and experiences a corresponding radiation-reaction force, or self force. We extend to higher order in the total charge a…

### Electromagnetic self-forces and generalized Killing fields

- Physics
- 2009

Building upon previous results in scalar field theory, a formalism is developed that uses generalized Killing fields to understand the behavior of extended charges interacting with their own…

### Radiation reaction in classical electrodynamics

- PhysicsPhysical Review D
- 2019

The Lorentz-Abraham-Dirac equations (LAD) may be the most commonly accepted equation describing the motion of a classical charged particle in its electromagnetic field. However, it is well known that…

### Combined gravitational and electromagnetic self-force on charged particles in electrovac spacetimes

- Physics
- 2014

We consider the self-force on a charged particle moving in a curved spacetime with a background electromagnetic eld, extending previous studies to situations in which gravitational and…

### Dependence of self-force on central object

- Physics
- 2011

For a particle in orbit about a static spherically symmetric body, we study the change in self-force that results when the central body type (i.e., the choice of interior metric for the Schwarzschild…

### Foundations of the self-force problem in arbitrary dimensions

- PhysicsPhysical Review D
- 2018

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…

### Curing the self-force runaway problem in finite-difference integration

- PhysicsPhysical Review D
- 2019

The electromagnetic self-force equation of motion is known to be afflicted by the so-called runaway problem. A similar problem arises in the semiclassical Einstein's field equation and plagues the…

### Field-free electrodynamics

- Physics
- 2018

The Maxwell-Lorentz theory of electrodynamics cannot readily be applied to a system of point charges: the electromagnetic field is not well-defined at the position of a point charge, an energy…

### The Motion of Point Particles in Curved Spacetime

- PhysicsLiving reviews in relativity
- 2011

The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch.

## References

SHOWING 1-10 OF 28 REFERENCES

### Self-forces on extended bodies in electrodynamics

- Physics
- 2006

In this paper, we study the bulk motion of a classical extended charge in flat spacetime. A formalism developed by W. G. Dixon is used to determine how the details of such a particle's internal…

### Gravitational radiation reaction to a particle motion

- Physics
- 1997

A small mass particle traveling in a curved spacetime is known to trace a background geodesic in the lowest order approximation with respect to the particle mass. In this paper, we discuss the…

### The Motion of Point Particles in Curved Spacetime

- PhysicsLiving reviews in relativity
- 2004

The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch.

### Dynamics of a charged particle.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

Using physical arguments, I derive the physically correct equations of motion for a classical charged particle from the Lorentz-Abraham-Dirac equations (LAD) which are well known to be physically…

### Motion of a small body through an external field in general relativity calculated by matched asymptotic expansions

- Physics
- 1980

This paper shows that a small body with possibly strong internal gravity moves through an empty region of a curved, and not necessarily asymptotically flat, external space-time on an approximate…

### Classical theory of radiating electrons

- Physics
- 1938

The Lorentz model of the electron as a small sphere charged with electricity, possessing mass on account of the energy of the electric field around it, has proved very valuable in accounting for the…

### Radiation Reaction in Nonrelativistic Quantum Electrodynamics

- Physics
- 1977

We derive the Heisenberg operator equation of motion for a nonrelativistic point electron coupled to the quantized electromagnetic field, including radiation reaction. The derivation proceeds in…

### Laws of motion and precession for black holes and other bodies.

- PhysicsPhysical review. D, Particles and fields
- 1985

This paper derives the largest corrections to the geodesic law of motion and Fermi-Walker law of transport, due to coupling of the body’s angular momentum and quadrupole moment to the Riemann curvature of the surrounding spacetime.

### The uniform circular motion with invariable normal spin of a rigidly and uniformly electrified sphere, IV

- Mathematics
- 1937

In order to exhibit clearly and fully the possibilities inherent in classical electrodynamics when it is developed rigorously without approximations or unnecessary restrictions I have in this paper…

### Gravitational Radiation Damping of Slowly Moving Systems Calculated Using Matched Asymptotic Expansions

- Mathematics
- 1971

This paper treats the slow‐motion approximation for radiating systems as a problem in singular perturbations. By using the method of matched asymptotic expansions, we can construct approximations…