Περίληψη:
The Mathisson-Papapetrou-Dixon (MPD) equations describe the motion of an
extended test body in general relativity. This system of equations,
though, is underdetermined and has to be accompanied by constraining
supplementary conditions, even in its simplest version, which is the
pole-dipole approximation corresponding to a spinning test body. In
particular, imposing a spin supplementary condition (SSC) fixes the
center of mass of the spinning body, i.e., the centroid of the body. In
the present study, we examine whether characteristic features of the
centroid of a spinning test body, moving in a circular equatorial orbit
around a massive black hole, are preserved under the transition to
another centroid of the same physical body, governed by a different SSC.
For this purpose, we establish an analytical algorithm for deriving the
orbital frequency of a spinning body, moving in the background of an
arbitrary, stationary, axisymmetric spacetime with reflection symmetry,
for the Tulczyjew-Dixon, the Mathisson-Pirani, and the
Ohashi-Kyrian-Semerak SSCs. Then, we focus on the Schwarzschild black
hole background, and a power series expansion method is developed in
order to investigate the discrepancies in the orbital frequencies
expanded in power series of the spin among the different SSCs. Lastly,
by employing the fact that the position of the centroid and the measure
of the spin alters under the centroid's transition, we impose proper
corrections to the power expansion of the orbital frequencies, which
allows to improve the convergence between the SSCs. Our concluding
argument is that when we shift from one circular equatorial orbit to
another in the Schwarzschild background, under the change of a SSC, the
convergence between the SSCs holds only up to certain powers in the spin
expansion, and it cannot be achieved for the whole power series.
Συγγραφείς:
Timogiannis, Iason
Lukes-Gerakopoulos, Georgios
Apostolatos,
Theocharis A.
