  Through a M\"obius transformation, we study aspects like topology, ligth
cones, horizons, curvature singularity, lines of constant Schwarzschild
coordinates $r$ and $t$, null geodesics, and transformed metric, of the
spacetime $(SKS/2)^\prime$ that results from: i) the antipode identification in
the Schwarzschild-Kruskal-Szekeres ($SKS$) spacetime, and ii) the suppression
of the consequent conical singularity. In particular, one obtains a non
simply-connected topology: $(SKS/2)^\prime\cong \mathbb{R}^{2*}\times S^2$ and,
as expected, bending light cones.
