First law of mechanics for spinning compact binaries: Dipolar order - INSPIRE

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First law of mechanics for spinning compact binaries: Dipolar order

Paul Ramond
(
- CEREMADE, Paris and
- LUTH, Meudon
)
,
Alexandre Le Tiec
(
- LUTH, Meudon
)

Feb 18, 2022

44 pages

Published in:

Phys.Rev.D 106 (2022) 4, 044057

Published: Aug 15, 2022

e-Print:

2202.09345 [gr-qc]

DOI:

10.1103/PhysRevD.106.044057 (publication)

View in:

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Abstract: (APS)

Building upon the Noether charge formalism of Iyer and Wald, we derive a variational formula for spacetimes admitting a Killing vector field for a generic energy-momentum distribution with compact support. Applying this general result to the particular case of a binary system of spinning compact objects moving along an exactly circular orbit, modeled using the multipolar gravitational skeleton formalism, we derive a first law of compact binary mechanics at dipolar order. We prove the equivalence of this new result with the canonical Hamiltonian first law previously derived for binary systems of spinning compact objects, for spins collinear with the orbital angular momentum. This paper paves the way to an extension of the first law of binary mechanics to the next quadrupolar order, thereby accounting for the spin- and tidally induced deformability of the compact bodies.

Note:

44 pages, 3 figures

References(89)

Figures(3)

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