The stress-energy distributional multipole for both uncharged and charged dust

Abstract

In this paper, we formulate the distributional uncharged and charged stress-energy tensors. These are integrals, along a worldline, of derivatives of the delta-function. These distributions are also multipoles and they are prescribed to any order. They represent an extended region of non-self-interacting uncharged or charged dust, shrunken to a single point in space. We show that the uncharged dust stress-energy multipole is divergence-free, while the divergence of the charged dust stress-energy multipole is given by the current and the external electromagnetic field. We show that they can be obtained by squeezing a regular dust stress-energy tensor onto the worldine. We discuss the aforementioned calculations in a coordinate-free manner.