Markus Wolff
We study the effects of the null energy condition on both spacelike and timelike umbilical hypersurfaces in a class of static spacetimes. In the spacelike case, we study umbilical warped product graphs and give a full characterization of embedded surfaces with constant spacetime mean curvature using an Alexandrov Theorem by Brendle. In the timelike case, we achieve a characterization of photon surfaces with constant umbilicity factor similar to a recent result by Cederbaum and Galloway.
