On effects of the null energy condition on totally umbilic hypersurfaces in a class of static spacetimes (Q6618813)

The null energy condition states that for any null vector field \(L\) the Einstein tensor \(G\) satisfies \(G(L, L) \geq 0\). This paper studies the consequences of this condition on both space-like and time-like totally umbilic hypersurfaces in a class of static warped product spacetimes. In the space-like case, the author obtains a full characterization of embedded surfaces with constant spacetime mean curvature using an Alexandrov theorem by \textit{S. Brendle} [Publ. Math., Inst. Hautes Étud. Sci. 117, 247--269 (2013; Zbl 1273.53052)] and \textit{S. Borghini} et al. [``The equality case in the substatic Heintze-Karcher inequality'', Preprint, \url{arXiv:2307.04253}]. In the time-like case, a characterization of photon surfaces with constant umbilicity factor is achieved.