Radiation Beyond Four Space-Time Dimensions

TL;DR

This paper derives formulas for classical radiation from accelerated point sources in even-dimensional flat space-times, enabling calculation of radiation characteristics for various tensor ranks and dimensions, with practical limitations for higher tensor ranks.

Contribution

It provides a comprehensive set of formulas for tensor field radiation in arbitrary even dimensions, facilitating analytical and computational evaluation of radiation properties.

Findings

Formulas for radiation of rank s tensor fields in arbitrary even dimensions.

Algorithmic approach to compute total intensity and momentum of radiation.

Limitations identified for s>1 due to non-conservation of energy-momentum tensor.

Abstract

We present a list of formulas describing classical radiation of the rank s tensor field from an accelerated point-like source in flat space-time of arbitrary even dimension d. This allows straightforward evaluating the total intensity and radiated momentum for any $s$ and $d$ algorithmically, by hands or with the help of a computer (e.g. with an attached MAPLE program). Practical application of formulas is limited, because, for s>1, the energy-momentum tensor for the point-like source is not conserved. This usually means that one cannot neglect contributions to radiation from tensions of the forces that cause acceleration of the source.