Lightlike shell solitons of extremal space-time film

TL;DR

This paper introduces a new class of exact lightlike soliton solutions in a nonlinear scalar field model, exhibiting properties similar to photons, including energy, angular momentum, and polarization effects.

Contribution

The paper presents a novel exact solution class of lightlike solitons with shell singularities in a Born-Infeld type model, linking soliton properties to quantum-like features.

Findings

Solitons propagate at light speed with calculable energy, momentum, and angular momentum.

The energy-angular momentum relation approximates the Planck constant for high-frequency twisted solitons.

The energy spectral density of a soliton gas resembles the Planck distribution.

Abstract

New exact solution class of Born -- Infeld type nonlinear scalar field model is obtained. The variational principle of this model has a specific form which is characteristic for extremal four-dimensional hypersurface or hyper-film in five-dimensional space-time. Obtained solutions are singular solitons propagating with speed of light and having energy, momentum, and angular momentum which can be calculated for explicit conditions. Such solitons will be called the lightlike ones. The soliton singularity has a form of moving two-dimensional surface or shell. The lightlike soliton can have a set of tubelike singular shells with the appropriate cavities. A twisted lightlike soliton is considered. It is notable that its energy is proportional to its angular momentum in high-frequency approximation. A case with one tubelike cavity is considered. In this case the soliton shell is diffeomorphic to a cylindrical surface with threads by multifilar helix. The shell transverse size of the appropriate finite energy soliton can be converging to zero at infinity. The ideal gas of such lightlike solitons with minimal twist parameter is considered in a finite volume. Explicit conditions provide that the angular momentum of each soliton in the volume equals Planck constant. The equilibrium energy spectral density for the solitons is obtained. It has the form of Planck distribution in some approximation. A beam of the twisted lightlike solitons is considered. The representation of arbitrary polarization for the beam with the twisted lightlike solitons is discussed. It is shown that the effect of mechanical angular momentum transfer to absorbent by the circularly polarized beam can be provided. This effect is well known for photon beam. Thus the soliton solution which have determinate likeness with photon is obtained in particular.