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Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - The distributional stress-energy quadrupole
AU - Gratus, Jonathan
AU - Pinto, Paolo
AU - Talaganis, Spyridon
PY - 2020/12/23
Y1 - 2020/12/23
N2 - We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on quadrupoles as they make an excellent model for the dominant source of gravitational waves and have significant novel features. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example motivated from a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the change of coordinate formula which involves second derivatives and two integrals. We also show how to define the quadrupole without reference to a coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a coordinate free way.
AB - We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on quadrupoles as they make an excellent model for the dominant source of gravitational waves and have significant novel features. Unlike the dipole, we show that the quadrupole has 20 free components which are not determined by the properties of the stress-energy tensor. These need to be derived from an underlying model and we give an example motivated from a divergent-free dust. We show that the components corresponding to the partial derivatives representation of the quadrupole, have a gauge like freedom. We give the change of coordinate formula which involves second derivatives and two integrals. We also show how to define the quadrupole without reference to a coordinate systems or a metric. For the representation using covariant derivatives, we show how to split a quadrupole into a pure monopole, pure dipole and pure quadrupole in a coordinate free way.
KW - de Rham Currents
KW - Gravitational wave sources
KW - general relativity
KW - gravity
KW - Coordinate free approach
KW - coordinate transformations
KW - stress energy tensors
U2 - 10.1088/1361-6382/abccde
DO - 10.1088/1361-6382/abccde
M3 - Journal article
VL - 38
JO - Classical and Quantum Gravity
JF - Classical and Quantum Gravity
SN - 0264-9381
IS - 3
M1 - 035011
ER -