Singularities from the Topology and Differentiable Structure of Asymptotically Flat Spacetimes

Understand

We prove that certain asymptotically flat initial data sets with nontrivial topology and/or differentiable structure collapse to form singularities.

• The class of such initial data sets is characterized by a new smooth invariant, the maximal Yamabe invariant, defined through smooth compactification of the asymptotically flat manifold.
• Our singularity theorem applies to spacetimes admitting a Cauchy surface of nonpositive maximal Yamabe invariant with initial data that satisfies the dominant energy condition.
• This class of spacetimes includes simply connected spacetimes with a single asymptotic region, a class not covered by prior singularity theorems for topological structures.