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Canonical formulation of spin in general relativity†
Article first published online: 16 FEB 2011
Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Annalen der Physik
Volume 523, Issue 4, pages 296–353, April 2011
How to Cite
Steinhoff, J. (2011), Canonical formulation of spin in general relativity. Ann. Phys., 523: 296–353. doi: 10.1002/andp.201000178
Dissertation, Friedrich-Schiller-Universität, Jena, 2010.
- Issue published online: 8 MAR 2011
- Article first published online: 16 FEB 2011
- Manuscript Accepted: 18 JAN 2011
- Manuscript Received: 30 DEC 2010
- DFG. Grant Numbers: SFB/TR7 “Gravitational Wave Astronomy”, GRK 1523 “Quantum and Gravitational Fields”
- Canonical formalism;
- post-Newtonian approximation;
- binary stars.
The present article aims at an extension of the canonical formalism of Arnowitt, Deser, and Misner from self-gravitating point-masses to objects with spin. This would allow interesting applications, e.g., within the post-Newtonian (PN) approximation. The extension succeeded via an action approach to linear order in the single spins of the objects without restriction to any further approximation. An order-by-order construction within the PN approximation is possible and performed to the formal 3.5PN order as a verification. In principle both approaches are applicable to higher orders in spin. The PN next-to-leading order spin(1)-spin(1) level was tackled, modeling the spin-induced quadrupole deformation by a single parameter. All spin-dependent Hamiltonians for rapidly rotating bodies up to and including 3PN are calculated.