Dynamical horizon

In theoretical physics, a dynamical horizon (DH) is a local description (i.e. independent of the global structure of the spacetime) of evolving black hole horizons. In the literature there exist two different mathematical formulations of DHs—the 2+2 formulation developed by Sean Hayward and the 3+1 formulation 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

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