Next-to-next-to-leading order post-Newtonian spin(1)-spin(2) Hamiltonian for self-gravitating binaries

We present the next‐to‐next‐to‐leading order post‐Newtonian (PN) spin(1)‐spin(2) Hamiltonian for two self‐gravitating spinning compact objects. If both objects are rapidly rotating, then the corresponding interaction is comparable in strength to a 4PN effect. The Hamiltonian is checked via the global Poincaré algebra with the center‐of‐mass vector uniquely determined by an ansatz. The authors present the next‐to‐next‐to‐leading order post‐Newtonian (PN) spin(1)‐spin(2) Hamiltonian for two self‐gravitating spinning compact objects. If both objects are rapidly rotating, then the corresponding interaction is comparable in strength to a 4PN effect. The Hamiltonian is checked via the global Poincaré algebra with the center‐of‐mass vector uniquely determined by an ansatz.