Spinning particles in general relativity: Momentum-velocity relation for the Mathisson-Pirani spin condition

0497137 - ASÚ 2019 RIV US eng J - Journal Article
Costa, L.F.O. - Lukes-Gerakopoulos, Georgios - Semerák, O.
Spinning particles in general relativity: Momentum-velocity relation for the Mathisson-Pirani spin condition.
Physical Review D. Roč. 97, č. 8 (2018), č. článku 084023. ISSN 2470-0010. E-ISSN 2470-0029
R&D Projects: GA ČR(CZ) GJ17-06962Y
Grant - others:GA ČR(CZ) GA17-13525S
Institutional support: RVO:67985815
Keywords : hidden momentum * kerr field * dynamics
OECD category: Astronomy (including astrophysics,space science)
Impact factor: 4.368, year: 2018

The Mathisson-Papapetrou-Dixon (MPD) equations, providing the pole-dipole description of spinning test particles in general relativity, have to be supplemented by a condition specifying the worldline that will represent the history of the studied body. It has long been thought that the Mathisson-Pirani (MP) spin condition-unlike other major choices made in the literature-does not yield an explicit momentum-velocity relation. We derive here the desired (and very simple) relation and show that it is in fact equivalent to the MP condition. We clarify the apparent paradox between the existence of such a definite relation and the known fact that the MP condition is degenerate (does not specify a unique worldline), thus shedding light on some conflicting statements made in the literature. We then show how, for a given body, this spin condition yields infinitely many possible representative worldlines, and derive a detailed method how to switch between them in a curved spacetime. The MP condition is a convenient choice in situations when it is easy to recognize its “nonhelical” solution, as exemplified here by bodies in circular orbits and in radial fall in the Schwarzschild spacetime.
Permanent Link: http://hdl.handle.net/11104/0289725