Isofrequency pairing of spinning particles in Schwarzschild–de Sitter spacetime

Abstract

It has been established in Schwarzschild spacetime (and more generally in Kerr spacetime) that pairs of geometrically different timelike geodesics with the same radial and azimuthal frequencies exist in the strong field regime. The occurrence of this socalled isofrequency pairing is of relevance in view of gravitational-wave observations. In this paper we generalize the results on isofrequency pairing in two directions. Firstly, we allow for a (positive) cosmological constant, i.e., we replace the Schwarzschild spacetime with the Schwarzschild-de Sitter spacetime. Secondly, we consider not only spinless test-particles (i.e., timelike geodesics) but also test-particles with spin. In the latter case we restrict to the case that the motion is in the equatorial plane with the spin perpendicular to this plane. We find that the cosmological constant as well as the spin have distinct impacts on the description of bound motion in the frequency domain.