Abstract:
Starting from the main definitions, we review the rigging technique for null hypersurfaces
theory and most of its main properties. We make some applications to illustrate it. On the one hand, we show how we can use it to show properties of null hypersurfaces, with emphasis in null cones, totally geodesic, totally umbilic, and compact null hypersurfaces. On the other hand, we show the interplay with the ambient space, including its influence in causality theory.
Description:
Null hypersurfaces are present in general relativity in several fundamental theories.
For example, the thermodynamic of black holes stated an unexpected link between classical
thermodynamic theory and black hole theory using the horizon of the black hole, which
is a null hypersurface [1–3].
