Applications of MPD
Applications of MPD
In this note, we aim to derive the MPD equations for the Schwarzschild metric. Then, we examine the conservation of several generalized quantities within the MPD system of equations, and finally, we study the evolution of the spin vector of a test particle moving in Schwarzschild spacetime.
The theoretical framework developed in this article is based on A. Papapetrou’s seminal paper Spinning Test Particles in General Relativity. In this article, a particular supplementary condition is adopted such that the spin tensor possesses only spatial components. This condition was commonly employed in the early studies of the motion of spinning particles in gravitational fields. However, it does not necessarily lead to physically acceptable solutions in all situations.
Indeed, the choice of supplementary condition plays a crucial role in the analysis of spinning-particle motion in curved spacetime, since an arbitrary supplementary condition does not necessarily yield physically meaningful results. In this note, we adopt one specific supplementary condition and, in subsequent notes, we will demonstrate that it can give rise to several peculiar and physically problematic features.