Isolated and dynamical horizons from a common perspective

Abstract

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 physicaly relevant quantities describing the horizon irrespective to whether it is isolated (null) or dynamical at a given instant of time. Furthermore, small perturbation of isolated horizons are considered, and finally a family of axially--symmetric exact solution of the constraint equations on a dynamical horizon is presented.

12 pages, one figure, revtex4. v2: added various references in introduction and sec. 2, short discussion of applicability to slowly evolving horizons in sec. 4B. Several minor corrections throughout text

References in corpus (2)

• Introduction to dynamical horizons in numerical relativity
• A generalized Damour-Navier-Stokes equation applied to trapping horizons

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• Quasi--local angular momentum of non--symmetric isolated and dynamical horizons from the conformal decomposition of the metric
• Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes
• Horizons in Robinson-Trautman space-times