Electromagnetic and Gravitational Radiation in All Dimensions: A Classical Field Theory Treatment

TL;DR

This paper derives classical electromagnetic and gravitational radiation formulas in all dimensions, revealing how wave tails affect signal duration and phase shifts in odd-dimensional spacetimes, with implications for understanding wave propagation.

Contribution

It provides the first classical field theory derivation of radiation formulas in all dimensions, clarifying the impact of tails on wave signals in odd-dimensional spacetimes.

Findings

In even dimensions, radiation depends only on retarded time derivatives.

In odd dimensions, radiation involves integrals over retarded histories.

Tails cause phase shifts and non-oscillatory transients in signals.

Abstract

How long does a light bulb shine in odd dimensional flat spacetimes, according to a distant observer? This question is non-trivial 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 non-oscillatory inverse square roots in time.