Isolated and dynamical horizons from a common perspective

A framework is developed in which one can write down the constraint equations on a three-dimensional hypersurface of arbitrary signature. It is then applied to isolated and dynamical horizons. The derived equations can be used to extract physically relevant quantities describing the horizon irrespective to whether it is isolated (null) or dynamical at a given instant of time. Furthermore, a small perturbation of isolated horizons are considered, and finally a family of an axially symmetric exact solution of the constraint equations on a dynamical horizon is presented.

Figure 1

Geometry of the horizon section.