Abstract
In this work, we use parallel transport of vectors to study global characteristics of the Schwarzschild spacetime, in the context of the five-dimensional Randall-Sundrum braneworld, in the spacetime known as black cigar. We examine constant time circular orbits, where the parallel transport matrix indicates the existence of the analogue gravitational Aharonov-Bohm effect, except for some particular radii, where this matrix is trivial. Parallel transport along radial and time displacements are also obtained, reducing, in all cases to the usual results of ordinary Schwarzschild spacetime. On the other hand, the parallel transport matrix for a circular orbit in the Schwarzschild-AdS spacetime, an alternative solution for the black hole on the brane, keeps a ``memory" of the higher dimension.
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