The tensorial representation of the distributional

Gratus, Jonathan and Talaganis, Spyridon (2023) The tensorial representation of the distributional. Classical and Quantum Gravity. ISSN 0264-9381 (In Press)

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Abstract

We investigate stress-energy tensors constructed from the covariant derivatives of delta functions on a worldline. Since covariant derivatives are used all the components transform as tensors. We derive the dynamical equations for the components, up to quadrupole order. The components do, however, depend in a non-tensorial way, on a choice of a vector along the worldline. We also derive a number of important results about general multipoles, including that their components are unique, and all multipoles can be written using covariant derivatives. We show how the components of a multipole are related to standard moments of a tensor field, by parallelly transporting that tensor field.