Canonical formulation of spin in general relativity

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.