Abstract

Totally geodesic null hypersurfaces have been widely used as models of time-independent event and isolated black hole horizons. However, in reality black hole being surrounded by a local mass distribution there is significant difference in the structure of the surrounding region of isolated black holes. In this paper, we use metric conformal symmetry which provides a class of a family of totally umbilical null hypersurfaces (Theorem 4), supported by a physical model and an example of time-dependent evolving null horizons (see Definition 6) conformally related to
an isolated black hole. We establish an interrelation between the spacelike dynamical horizons (see Definition 7), isolated and evolving null horizons. Finally we propose further study on null geometry and physics of the surface closer to an isolated horizon.

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