The ultrarelativistic Reissner-Nordstrom field in the Colombeau algebra

TL;DR

This paper uses Colombeau's theory to analyze the ultrarelativistic Reissner-Nordstrom electromagnetic field, revealing that delta-like energy densities are mathematically consistent despite being physically unsatisfactory.

Contribution

It demonstrates that delta-like energy densities in ultrarelativistic fields are mathematically well-defined within Colombeau's nonlinear generalized functions framework.

Findings

The field tensor vanishes while energy density is delta-like.

Such distributional energy densities are unavoidable in this context.

Mathematically consistent description of ultrarelativistic fields with singular energy profiles.

Abstract

The electromagnetic field of the ultrarelativistic Reissner-Nordstrom solution shows the physically highly unsatisfactory property of a vanishing field tensor but a nonzero, i.e., delta-like, energy density. The aim of this work is to analyze this situation from a mathematical point of view, using the framework of Colombeau's theory of nonlinear generalized functions. It is shown that the physically unsatisfactory situation is mathematically perfectly defined and that one cannot aviod such situations when dealing with distributional valued field tensors.