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 <br />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.
Highlights
Considerable work has been done on time-independent isolated black hole physics of asymptotically flat spacetimes which is still an active area of research
Let S = ((Hu),) be a family of null hypersurfaces of a family F = (M, (Gs)) of spacetimes defined by (3) whose each memeber is conformally related to an isolated black hole spacetime (M, g), with an isolated horizon (H, q) as defined by (1), which lies to the future of each (Hu, hu)
We first recall that for more than 50 years the research on black hole physics was limited to time-independent event and isolated horizons until first attempt on time-dependent horizons was made by (Hayward, 1994) describing the geometry of the surface of dynamical black hole by using the following definition of future, outer, trapping horizons
Summary
Considerable work has been done on time-independent isolated black hole physics of asymptotically flat spacetimes which is still an active area of research. Such isolated black holes deal with the concept of an event and isolated horizons briefly explained as follows: Event horizons. Attempts have been made to find a quasilocal concept of a horizon which requires only minimum number of conditions to detect a black hole and study its properties. For this purpose, (Asktekar et al, 1999) introduced following three notions of “Isolated Horizons”
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