Energy, momentum and angular momentum conservations in de Sitter special relativity

TL;DR

This paper explores conserved currents in de Sitter special relativity, deriving two types of angular momentum currents and predicting an inherent energy-momentum tensor, contrasting these with ordinary Lorentz-invariant special relativity.

Contribution

It introduces two novel conserved current types in de Sitter SR and predicts an inherent energy-momentum tensor from the spin part of the covariant current.

Findings

Derived a 5d dS-covariant angular momentum current.

Generalized a dS-invariant angular momentum current for matter and gravity.

Predicted an inherent energy-momentum tensor from spin contributions.

Abstract

In de Sitter (dS) special relativity (SR), two kinds of conserved currents are derived. The first kind is a 5-dimensional (5d) dS-covariant angular momentum (AM) current, which unites the energy-momentum (EM) and 4d AM current in an inertial-type coordinate system. The second kind is a dS-invariant AM current, which can be generalized to a conserved current for the coupling system of the matter field and gravitational field in dS gravity. Moreover, an inherent EM tensor is predicted, which comes from the spin part of the dS-covariant current. All the above results are compared to the ordinary SR with Lorentz invariance.