A hairy extension of the Bertotti-Robinson regular spacetime has been
recently introduced in the context of the Einstein-Maxwell-Scaler theory
that surprisingly is a singular black hole formed in the $S_{3}$ background
spatial topology [CQG39(2022)167001]. In this research, we first clarify the
topology of the spacetime based on the coordinate transformations as well as
the energy-momentum configuration and the causal structure of the black
hole. Furthermore, we investigate the geodesics of the null and timelike
particles in this spacetime. It is shown that in the radial motion on the
equatorial plane, while photons may collapse to the singularity or escape to
the edge of the universe, a massive particle always collapses to the
singularity. The general geodesics of null and massive particles reveal that
all particles except the outgoing light ray, eventually fall into the black
hole.
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