First Law of Mechanics for Spinning Compact Binaries: Dipolar Order
arXiv:2202.09345 · doi:10.1103/PhysRevD.106.044057
Abstract
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, modelled 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 colinear 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-induced and tidally-induced deformability of the compact bodies.
44 pages, 3 figures
References in corpus (11)
- Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
- Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling
- Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binaries
- Circular orbits and spin in black-hole initial data
- Waveless Approximation Theories of Gravity
- Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole
- Two-body gravitational spin-orbit interaction at linear order in the mass ratio
- An introduction to relativistic hydrodynamics
- Tidal invariants for compact binaries on quasi-circular orbits
- Multi-Domain Spectral Method for Initial Data of Arbitrary Binaries in General Relativity
- Thermodynamics of magnetized binary compact objects