Foliation of null cones by surfaces of constant spacetime mean curvature near MOTS

Marginally Outer Trapped Surfaces (MOTS) in spacetimes are well-known to indicate the existence of black holes. Using flow techniques, we prove that a neighbourhood of a stable MOTS in a null cone may be foliated by hypersurfaces of constant spacetime mean curvature. We also provide methods to construct prescribed spacetime mean curvature surfaces within null cones.