TY - JOUR

T1 - The tensorial representation of the distributional stress–energy quadrupole and its dynamics

AU - Gratus, Jonathan

AU - Talaganis, Spyridon

PY - 2023/4/20

Y1 - 2023/4/20

N2 - 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.

AB - 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.

KW - Physics and Astronomy (miscellaneous)

U2 - 10.1088/1361-6382/acc163

DO - 10.1088/1361-6382/acc163

M3 - Journal article

VL - 40

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 8

M1 - 085012

ER -