Canonical Formulation of Spin in General Relativity

Abstract

The present thesis 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.

59 pages. Dissertation, Friedrich-Schiller-Universität, Jena, 2010. This thesis was submitted in June 2010. Cite as Ann. Phys. (Berlin) 523:296 (2011)

References in corpus (17)

• Tests of general relativity from timing the double pulsar
• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-spinning, equal-mass black holes
• xPerm: fast index canonicalization for tensor computer algebra
• 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
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux
• Effective field theory calculation of second post-Newtonian binary dynamics
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• ADM canonical formalism for gravitating spinning objects
• Nonrotating black hole in a post-Newtonian tidal environment
• Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance
• Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. IV. Radiation reaction for binary systems with spin-spin coupling
• A LISA Data-Analysis Primer
• Application of energy and angular momentum balance to gravitational radiation reaction for binary systems with spin-orbit coupling
• Comment on recent papers regarding next-to-leading order spin-spin effects in gravitational interaction