Particle Motion under the Conservative Piece of the Self-Force is Hamiltonian
Francisco M. Blanco, Éanna É. Flanagan
Abstract
We consider the motion of a point particle in a stationary spacetime under the influence of a scalar, electromagnetic, or gravitational self-force. We show that the conservative piece of the first-order self-force gives rise to Hamiltonian dynamics, and we derive an explicit expression for the Hamiltonian on phase space. Specialized to the Kerr spacetime, our result generalizes the Hamiltonian function previously obtained by Fujita et al. [Classical Quantum Gravity 34, 134001 (2017).CQGRDG0264-938110.1088/1361-6382/aa7342], which is valid only for nonresonant orbits.
Topics & Concepts
PhysicsHamiltonian (control theory)Classical mechanicsPhase spacePoint particleSpacetimeHamiltonian mechanicsGravitationCovariant Hamiltonian field theoryQuantumMathematical physicsQuantum mechanicsHamiltonian systemMathematicsMathematical optimizationPulsars and Gravitational Waves ResearchCosmology and Gravitation TheoriesNoncommutative and Quantum Gravity Theories