Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution

Understand

In this work we initiate the mathematical study of naked singularities for the Einstein vacuum equations in $3+1$ dimensions by constructing solutions which correspond to the exterior region of a naked singularity.

• A key element is our introduction of a new type of self-similarity for the Einstein vacuum equations.
• Connected to this is a new geometric twisting phenomenon which plays the leading role in singularity formation.
• Prior to this work, the only known examples of naked singularities were the solutions constructed by Christodoulou for the spherically symmetric Einstein-scalar-field system, as well as other solutions explored numerically for either the spherically symmetric Einstein equations coupled to suitable matter models or for the Einstein equations in higher dimensions.