The degenerate nature of the metric on null hypersurfaces creates many difficulties
when attempting to define a covariant derivative on null submanifolds. This dissertation
investigates these challenges and provides a technique for defining a connection on null
hypersurfaces in some cases. Recent approaches using decomposition to define a covariant
derivative...
The degenerate nature of the metric on null hypersurfaces makes it difficult to define a covariant derivative on null submanifolds. Recent approaches using decomposition to define a covariant derivative on null hypersurfaces are investigated, with examples demonstrating the limitations of the methods. Motivated by Geroch’s work on asymptotically flat spacetimes,...