- 2005.02688v1
Accepted author manuscript, 433 KB, PDF document

Research output: Contribution to Journal/Magazine › Journal article

Published

**The Distributional Stress-Energy Quadrupole.** / Gratus, Jonathan; Pinto, Paolo; Talaganis, Spyridon.

Research output: Contribution to Journal/Magazine › Journal article

Gratus, J., Pinto, P., & Talaganis, S. (2020). The Distributional Stress-Energy Quadrupole. *arxiv.org*.

@article{1bf135b0670c43ac8a80acebeefe8eb2,

title = "The Distributional Stress-Energy Quadrupole",

abstract = " We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on the quadrupole which has up to two partial or derivatives of the delta function. 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 modelling 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 a second derivative 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. ",

keywords = "de Rham Currents, gravity, Gravitational waves",

author = "Jonathan Gratus and Paolo Pinto and Spyridon Talaganis",

note = "38 pages, 2 figures",

year = "2020",

month = may,

day = "6",

language = "English",

journal = "arxiv.org",

}

TY - JOUR

T1 - The Distributional Stress-Energy Quadrupole

AU - Gratus, Jonathan

AU - Pinto, Paolo

AU - Talaganis, Spyridon

N1 - 38 pages, 2 figures

PY - 2020/5/6

Y1 - 2020/5/6

N2 - We investigate stress-energy tensors constructed from the delta function on a worldline. We concentrate on the quadrupole which has up to two partial or derivatives of the delta function. 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 modelling 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 a second derivative 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 the quadrupole which has up to two partial or derivatives of the delta function. 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 modelling 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 a second derivative 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 - gravity

KW - Gravitational waves

M3 - Journal article

JO - arxiv.org

JF - arxiv.org

ER -