Tearing the Fabric of Space

Einstein's general relativity says no, the fabric of space cannot tear. The equations of general relativity are firmly rooted in Riemannian geometry and, this is a framework that analyzes distortions in the distance relations between nearby locations in space. In order to speak meaningfully about these distant relations, the underlying mathematical formalism requires that the substrate of space is smooth--a term with a technical mathematical meaning, but whose every-day usage captures its essence: no creases, no punctures, no separate pieces "stuck" together, and no tears. Where the fabric of space to develop such irregularities, the equations of general relativity would break down, signaling some or other variety of cosmic catastrophe---a disastrous out-come that our apparently well-behaved universe avoids.