Electromagnetic and gravitational radiation in all dimensions: A classical field theory treatment

How long does a light bulb shine in odd dimensional flat spacetimes, according to a distant observer? This question is nontrivial because electromagnetic and gravitational waves, despite being comprised of massless particles, can develop tails; they travel inside the light cone. To this end, I attempt to close a gap in the literature by first deriving, strictly within classical field theory, the real-time electromagnetic dipole and gravitational quadrupole energy and angular momentum radiation formulas in all relevant dimensions. The even-dimensional case, where massless signals travel strictly on the null cone, depends on the time derivatives of the dipoles and quadrupoles solely at retarded time, whereas the odd-dimensional ones involve an integral over their retarded histories. Despite the propagation of light inside the null cone, however, I argue that a monochromatic light bulb of some intrinsic duration in odd dimensions remains approximately the same apparent duration to a distant detector, though the tail effect does produce a phase shift and adds to the signal several transitory nonoscillatory inverse square roots in time. Analogous remarks apply to a distant gravitational wave detector hearing from a finite duration quasiperiodic quadrupole source.