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).[1] It provides a description of a black hole that is evolving (e.g. one that has a non-zero mass-energy influx).[1] A related formalism, for black holes with zero influx, is an isolated horizon.

Formal definitionEdit

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

See alsoEdit



  1. ^ a b Duggal & Şahin 2010, p. 118.

Sources usedEdit

  • Duggal, Krishan L.; Şahin, Bayram (2010). "Dynamical horizons". Differential geometry of lightlike submanifolds. Springer. ISBN 978-3-0346-0250-1.CS1 maint: ref=harv (link)

Further readingEdit

Broad outlinesEdit

Major papersEdit

Other workEdit