Conclusion

Bondi and Gold’s solution to their problem was to say that there is no such thing as a static homogeneous gravitational field throughout the whole of spacetime, so one did not have to worry about the fact that the generally accepted strong equivalence principle implies that a charge that is stationary relative to standard coordinates for such a spacetime, in which the metric components happen to be independent of the time coordinate, is predicted to radiate electromagnetic energy. Although this solution looks rather weak, it would seem that Bondi and Gold were the only ones among the cited authors who understood the seriousness of the threat to the strong equivalence principle, without which one has no obvious way of doing electromagnetism in a general relativistic framework.

What Bondi and Gold really objected to was the idea that a charge that is stationary relative to coordinates in which the metric components of a spacetime are static should be able to radiate electromagnetic energy. The present thesis is that it would have been better to reject this as a pre-general-relativistic prejudice and treat the unrealistic case of a static homogeneous gravitational field as an application par excellence of the strong equivalence principle. Indeed, the spacetime is flat, so the locally inertial frames that are always promised by the weak equivalence principle, which in turn always holds in torsion-free spacetimes, turn out to be global inertial frames. According to the strong equivalence principle, a charged particle sitting still relative to the usual coordinates for this spacetime will be observed to radiate electromagnetic energy as viewed from the globally available inertial frames in precisely the same way that an eternally uniformly accelerating charge in a flat spacetime with no gravitational effects, not even non-tidal ones, will be observed to radiate such energy.