Dynamical horizon

                                    In theoretical physics, in particular in numerical relativity, a dynamical horizon (DH) is a mathematical formalism that was originally developed by Abhay Ashtekar and others (see Ashtekar & Krishnan 2004).It provides a description of a black hole that is evolving (e.g. one that has a non-zero mass-energy influx). A related formalism, for black holes with zero influx, is an isolated horizon.

The formal definition of a dynamical horizon is as follows:

A smooth, three-dimensional, space-like submanifold (possibly with boundary) Σ of space-time M is said to be a dynamical horizon if it can be foliated by a family of closed 2-manifolds such that on each leaf L

• the expansion Θ(ℓ) of one null normal ℓ is zero (i.e. it vanishes); and
• the expansion Θ(n) of the other null normal n is negative.