Extended bodies moving on geodesic trajectories

Abstract

In this article, we study the motion of an extended object in various spacetime geometries consists of the monopole, dipole as well as quadrupole moment within the framework of the general theory of relativity. We focus on a compelling limiting case, in which the acceleration of extended object vanishes and therefore, it becomes indistinguishable from a geodesic trajectory. In this case, both dipole, as well as the quadrupole moment of the extended object, would necessarily interact with the various moments of the central object, resulting in zero acceleration. We show that an object with monopole and dipole moment, namely the spin, can have a limit where the dipole-monopole and dipole-dipole interaction between that particle and the central object respectively vanishes. However, the introduction of quadrupole moment leads to more complicated situations and only the quadrupole-monopole interaction consists of a well-posed vanishing limit, while other interactions such as dipole-quadrupole or quadrupole-quadrupole, in general, remain nonzero. We expand on these scenarios in detail with their possible physical implications.