Spinning particles in Schwarzschild–de Sitter space–time

Abstract

After considering the reference case of the motion of spinning test bodies in the equatorial plane of the Schwarzschild space-time, we generalize the results to the case of the motion of a spinning particle in the equatorial plane of the Schwarzschild-de Sitter space-time. Specifically, we obtain the loci of turning points of the particle in this plane. We show that the cosmological constant affect the particle motion when the particle distance from the black hole is of the order of the inverse square root of the cosmological constant.

Highly relativistic spin-gravity- Λ coupling

“…Taking (3) into account it is easy to see that the right-hand side of (39) contains the gravitomagnetic components. For comparison, we present the relationship which follows from the rigorous MP equations (22) under condition (24). Taking into account the condition of the Fermi transport for the local orthogonal vectors γ (i)(k)(4) = 0 we write this relationship as [31] a (1)…”

“…In this context we note that on the circular orbits with u ⊥ = const expression (38) is rigorous, in contrast to the noncircular orbits when (38) is within the linear spin approximation. In the following we will consider rigorous MP equations (22) and (23) under condition (24).…”

“…(relationship (53) follows directly from the first equation from (22), with λ = 1). In addition to (53), it is necessary to take into account the relationship for u 3 and u 4…”

“…is determined just by the term u µ DS λµ ds (62) from the left-hand side of (22) and in the right-hand side of (26). The second one is that for the considered circular orbit with r = 3M both term (61) and (62) are equal to 0.…”

“…and then the gravitational attraction is compensated by the cosmological repulsion. The MP equations with condition (25) were studied in [22] to find the location of the turning points when a spinning particle is moving in the equatorial plane of the Schwarzschild-de Sitter metric. The specific case with the isofrequency pairing of spinning particles in the Schwarzschild-de Sitter background was investigated by the MP equations under condition (25).…”