Antipodal identification in the Schwarschild spacetime

Abstract

Through a Möbius 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: $(SKS/2{)}^{\prime }\cong {\mathbb{R}}^{2\ast }\times S^2$ and, as expected, bending light cones.

9 pages, 4 figures