  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.
