Exact self-similar solutions in Born-Infeld theory

TL;DR

This paper introduces new exact self-similar solutions in Born-Infeld theory, describing electromagnetic disturbances and electron-positron avalanches, with potential applications to scalar fields in higher-dimensional space-times.

Contribution

The paper presents a novel class of self-similar solutions in Born-Infeld electrodynamics with cylindrical and spherical symmetry, including a model for vacuum breakdown and particle avalanche propagation.

Findings

Cylindrical solutions describe electromagnetic disturbances in a magnetic background.

Solutions correspond to vacuum breakdown and electron-positron avalanche propagation.

Method extends to scalar Born-Infeld fields in higher-dimensional Minkowski space.

Abstract

We present a new class of exact self-similar solutions possessing cylindrical or spherical symmetry in Born-Infeld theory. A cylindrically symmetric solution describes the propagation of a cylindrical electromagnetic disturbance in a constant background magnetic field in Born-Infeld electrodynamics. We show that this solution corresponds to vacuum breakdown and the subsequent propagation of an electron-positron avalanche. The proposed method of finding exact analytical solutions can be generalized to the model of a spherically symmetric scalar Born-Infeld field in the ($n+1$)-dimensional Minkowski space-time. As an example, the case $n=3$ is discussed.