Blanco FM, Flanagan ÉÉ. Particle Motion under the Conservative Piece of the Self-Force is Hamiltonian.
Phys Rev Lett 2023;
130:051201. [PMID:
36800446 DOI:
10.1103/physrevlett.130.051201]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 12/06/2022] [Indexed: 06/18/2023]
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.
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