Does a Charged Particle in
Free Fall Radiate?

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Classical Radiation from a Uniformly Accelerated Charge, Thomas Fulton, Fritz Rohrlich, Annals of Physics: 9, 499-517 (1960)

5. Does Radiation In Hyperbolic Motion Contradict The Principle of Equivalence?

[...]. The solution to this apparent difficulty is to be found by considering an actual measurement of radiation, using our definition in Section3. Radiation is defined by the behavior of the fields in the limit of large distances from the source. Correspondingly, an observer who wants to detect the radiation cannot do so in the neighborhood of the particle's geodesic. Rather, he must be at a large distance from it, where gravitational fields have different values. The principle of equivalence, however, is a locally valid principle, referring to the geodesic of the particle, whereas the discussion above shows that an observation of radiation is not a local observation.

[...] Whatever gravitational field we introduce for the purpose of comparing it with an inertial field, we must be sure to have a distribution of distant stars which define our inertial systems. This means in particular that any homogeneous gravitational field is necessarily of finite extent, imbedded as it were, in an inertial coordinate system. We remark parenthetically that an infinite homogeneous gravitational field does not exist within the framework of general relativity either. The nonexistence of infinite homogeneous gravitational fields assures us that observation of radiation (observer at large distance from the source) takes place outside the homogeneous part of the gravitational field.

[...] "An electron which falls freely in a uniform gravitational field embedded in an inertial frame will radiate, and one which sits at rest on a table in the same field will not radiate; and these two statements do not contradict each other."

See also Principle of Equivalence, F. Rohrlich, Ann. Phys. 22, 169-191, (1963), page 173

Radiation Damping in a Gravitational Field, Bryce S. DeWitt, Robert W. Brehme, Annals of Physics: 9, 220-259 (1960)

The charged particle tries to do its best to satisfy the equivalence principle, and on a local basis, in fact, does so. In the absence of an externally applied electromagnetic field the motion of the particle deviates from geodetic motion only because of the unavoidable tail in the propagation function of the electromagnetic field, which enters into the picture nonlocally by appearing in an integral over the past history of the particles.

Principle of Equivalence, F. Rohrlich, Annals of   Physics: 22, 169-191, (1963), page 173

(C₃) An acceleration field is locally equivalent to a gravitational field.¹³

[...]

If one argues on the basis of (C₃) that this situation involves an accelerated charge which should always radiate, the argument is erroneous, because the fact that a charge is accelerated does not necessarily imply that it radiates, unless the acceleration takes place relative to an inertial observer. A noninertial observer uses different clocks and yardsticks. Thus, even though the charge is accelerated, it follows that, because the observer is also accelerated, the co-accelerated observer sees no radiation. Since radiation is not a generally covariant concept the question whether the charge really radiates is meaningless unless it is referred to a particular coordinate system. Finally, since the Schwarzschild metric, locally, for small G, and nonrelativsitically, is identical with the [static homogeneous gravitational field] metric, the above conclusion also holds for a charge at rest as seen by an observer in a Schwarzschild field.

[Footnote page 185: "An inertial frame in which there is a gravitational field present" is meaningless and self-contradictory"]

Radiation from an Accelerated Charge and the Principle of Equivalence, A. Kovetz and G.E. Tauber, Am. J. Phys., Vol. 37(4), April 1969

Abstract: The connection between an accelerated charge and one at rest in a (weak) gravitational field is discussed in accordance with the principle of equivalence principle. For that purpose, the fields produced by a freely falling charge and a supported one (i.e. at rest in a gravitational field) are transformed to the rest frame of the observer, who may be similarly supported or freely falling. A nonvanishing energy flux is found only if the charge is freely falling and the observer supported, or vice versa. This agrees with previously established results.

[...]

It may be interesting to discuss the foregoing results from a different view point - that of the photon picture: Is it possiible that one of the two observers we have been considering counts a number of photons, while the other, looking at the same charge, does not encounter any of them? In order to answer this question we take the case of a supported charge and the supported observer. Projecting the four-potential of the Born field onto the orthonormal tetrad carried by the supported observer, we find that only the fourth component is different than zero. This means that a radiation detector carried by the observer will not record any transitions in which transverse photons are involved. This is the quantum electrodynamical explanation for the absence of radiation from the supported charge.  It is not enough that photons are there; to be observable, they must be of the transverse kind, and this property (like the nonvanishing of a magnetic field) is not Lorentz invariant.

Radiation from a Uniformly Accelerated Charge, David G. Boulware, Annals of Physics: 124, 169-188 (1980)

Abstract: The electromagnetic field associated with a uniformly accelerated charge   is studied in some detail. The equivalence principle paradox that the   co-accelerating observer measures no radiation while a freely falling observer measures the standard radiation of an accelerated charge is resolved by noting that all the radiation goes into the region of space time inaccessible to the co-accelerating observer.

Hawking-Unruh Radiation and Radiation of a Uniformly Accelerated Charge, Kirk T. MacDonald, Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544

Abstract: ...an accelerated observer in a gravity-free environment experiences the same physics (locally) as an observer at rest in a gravitational field. Therefore, an accelerated observer (in zero gravity) should find him (her) self in a thermal bath of radiation characterized by temperature

T = hbar*a/2pck

where a is the acceleration as measured in the observer’s instantaneous rest frame.

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