# RADIATION DAMPING IN A GRAVITATIONAL FIELD

## Abstract

The validity of the principle of equivalence is examined relative to a charged mass point moving in an externally given gravitational field. The precedure is a covariant generalization of Dirac's work on the classical radiating electron. Just as Dirac's calculation was kept Lorentz invariant throughout, the present calculation is maintained generally covariant throughout. With the aid of bi-tensors, which are nonlocal generalizations of ordinary local tensors, the manifest general covariance of each step is achieved. The Green's functions for the scalar and vector wave equations in a curved manifold are obtained and applied to the derivation of the covariant Lienard-Wiechert potentials. The computation of energy-momentum balance across a world tube of infinitesimal radius surrounding the particle world-line then leads to the ponderomotive equations including radiation damping. Because of the nonlocal electromagnetic field which a charged particle carries with itself, its use as a device to distinguish locally between gravitational and inertial fields is really not allowable. An explicit occurrence of the Riemann tensor in the ponderomotive equations is found which shows that acceleration by a "true" gravitational field can produce bremsstrahlung, thereby causing a reactive force in addition to the force of inertia. The particle tries to satisfy the equivalencemore »

- Authors:

- Publication Date:

- Research Org.:
- Univ. of North Carolina, Chapel Hill

- OSTI Identifier:
- 4191447

- NSA Number:
- NSA-14-009894

- Resource Type:
- Journal Article

- Journal Name:
- Annals of Physics (New York) (U.S.)

- Additional Journal Information:
- Journal Volume: Vol: 9; Other Information: Orig. Receipt Date: 31-DEC-60

- Country of Publication:
- Country unknown/Code not available

- Language:
- English

- Subject:
- PHYSICS; ASTROPHYSICS; BREMSSTRAHLUNG; CHARGED PARTICLES; DIRAC EQUATIONS; ELECTROMAGNETIC FIELDS; ENERGY; EQUATIONS; FIELD THEORY; GRAVITATION; GREEN FUNCTION; LIENARD-WIECHERT POTENTIAL; MATHEMATICS; MOMENTUM; MOTION; NUMERICALS; QUANTUM MECHANICS; RADIATIONS; RECOILS; RELATIVITY THEORY; RIEMANN SPACE; SPACE; TENSORS; VECTORS

### Citation Formats

```
DeWitt, B.S., and Brehme, R.W..
```*RADIATION DAMPING IN A GRAVITATIONAL FIELD*. Country unknown/Code not available: N. p., 1960.
Web. doi:10.1016/0003-4916(60)90030-0.

```
DeWitt, B.S., & Brehme, R.W..
```*RADIATION DAMPING IN A GRAVITATIONAL FIELD*. Country unknown/Code not available. doi:10.1016/0003-4916(60)90030-0.

```
DeWitt, B.S., and Brehme, R.W.. Mon .
"RADIATION DAMPING IN A GRAVITATIONAL FIELD". Country unknown/Code not available. doi:10.1016/0003-4916(60)90030-0.
```

```
@article{osti_4191447,
```

title = {RADIATION DAMPING IN A GRAVITATIONAL FIELD},

author = {DeWitt, B.S. and Brehme, R.W.},

abstractNote = {The validity of the principle of equivalence is examined relative to a charged mass point moving in an externally given gravitational field. The precedure is a covariant generalization of Dirac's work on the classical radiating electron. Just as Dirac's calculation was kept Lorentz invariant throughout, the present calculation is maintained generally covariant throughout. With the aid of bi-tensors, which are nonlocal generalizations of ordinary local tensors, the manifest general covariance of each step is achieved. The Green's functions for the scalar and vector wave equations in a curved manifold are obtained and applied to the derivation of the covariant Lienard-Wiechert potentials. The computation of energy-momentum balance across a world tube of infinitesimal radius surrounding the particle world-line then leads to the ponderomotive equations including radiation damping. Because of the nonlocal electromagnetic field which a charged particle carries with itself, its use as a device to distinguish locally between gravitational and inertial fields is really not allowable. An explicit occurrence of the Riemann tensor in the ponderomotive equations is found which shows that acceleration by a "true" gravitational field can produce bremsstrahlung, thereby causing a reactive force in addition to the force of inertia. The particle tries to satisfy the equivalence principle in spite of its charge. It is only prevented from doing so (i,e., from following a geodetic path) because the electromagnetic Green's function in a curved spacetime does not generally vanish inside the light cone, but gives rise to a "tail" on any initially sharp pulse of radiation. The ponderomotive equations have exactly the same form as Dirac found for the flat-space-time case except for the addition of an integral over the entire past history of the particle, representing the effect of the "tail." (auth)},

doi = {10.1016/0003-4916(60)90030-0},

journal = {Annals of Physics (New York) (U.S.)},

number = ,

volume = Vol: 9,

place = {Country unknown/Code not available},

year = {1960},

month = {2}

}