Abstract
The dynamics of spinning particles in curved space–time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space–time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern–Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.
Highlights
The dynamics of spinning particles in curved space–time is discussed, emphasizing the hamiltonian formulation
The dynamics of angular momentum and spin of gravitating compact bodies has been a subject of great interest and intense investigation since the early days of relativity theory [1,2,3,4,5,6,7,8,9,10,11,12]; for recent overviews see [13,14,15]
One of the advantages of this description is that it can be applied to compact bodies with different types of spin dynamics, such as different gravimagnetic ratios
Summary
The dynamics of angular momentum and spin of gravitating compact bodies has been a subject of great interest and intense investigation since the early days of relativity theory [1,2,3,4,5,6,7,8,9,10,11,12]; for recent overviews see [13,14,15]. The other approach is to construct effective equations of motion for point-like objects, which is an idealization of a compact body, at the price of neglecting details of the internal structure by assigning the point-like object an overall position, momentum and spin. This is known as the spinning-particle approximation, and is used for the semi-classical description of elementary particles as well. One of the advantages of this description is that it can be applied to compact bodies with different types of spin dynamics, such as different gravimagnetic ratios In this way specific aspects of the structure can still be accounted for
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