The Equivalence Principle and an Electric Charge in a Gravitational Field II. A Uniformly Accelerated Charge Does Not Radiate

Details The Equivalence Principle and an Electric Charge in a Gravitational Field II. A Uniformly Accelerated Charge Does Not Radiate The Equivalence Principle and an Electric Charge in a Gravitational Field II. A Uniformly Accelerated Charge Does Not Radiate

Nov 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997gregr..29.1371s&link_type=abstract

General Relativity and Gravitation, Volume 29, Issue 11, p.1371-1390

Computer Science

11

Scientific paper

The electromagnetic field of a charge supported in a uniform gravitational field is examined from the viewpoint of an observer falling freely in the gravitational field. It is argued that such a charge, which from the principle of equivalence is moving with a uniform acceleration with respect to the freely falling (inertial) observer, could not be undergoing radiation losses at a rate implied by Larmor's formula. It is explicitly shown that the total energy in electromagnetic fields, including both velocity and acceleration fields, of a uniformly accelerated charge, at any given instant of the inertial observer's time, is just equal to the self-energy of a non-accelerated charge moving with a velocity equal to the instantaneous ``present'' velocity of the accelerated charge. It is further shown that at any given instant of time, and as seen with respect to the ``present'' position of the uniformly accelerated charge, although during the acceleration phase there is a radially outward component of the Poynting vector, there is throughout a {\it radially inward\/} Poynting flux component during the {\it deceleration\/} phase, and a null Poynting vector at the instant of the turn around. >From Poynting's theorem, which is defined for any region of space strictly in terms of {\it fixed instants\/} of time, it is shown that a uniformly accelerated charge does not emit electromagnetic radiation, in contrast to what is generally believed. It is further shown that, contrary to some earlier suggestions in the literature, there is no continuous passing of electromagnetic radiation from a uniformly accelerated charge into the region inaccessible to a co-accelerating observer. A comparison is made of the electric field distributions of a supported charge versus that of a freely falling charge in a uniform gravitational field.

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