Dynamical horizon

Formal definition

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.— Definition 3.3.2, Duggal & Şahin 2010, p. 118