Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations

Abstract

We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible evolutions and their deformations as well as derive the well-known flux laws. Using this framework, we unify much of what is already known about these objects as well as derive some new results. In particular we characterize and study the "almost-isolated" trapping horizons known as slowly evolving horizons. It is for these horizons that a dynamical first law holds and this is analogous and closely related to the Hawking-Hartle formula for event horizons.

39 pages, 6 figures, version to appear in PRD : a few minor changes and many typos corrected in equations

References in corpus (7)

• Introduction to dynamical horizons in numerical relativity
• A generalized Damour-Navier-Stokes equation applied to trapping horizons
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• Angular momentum conservation for dynamical black holes
• Symmetric non-expanding horizons
• Isolated and dynamical horizons from a common perspective
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Cited by in corpus (11)

• Extremality conditions for isolated and dynamical horizons
• Black holes and black hole thermodynamics without event horizons
• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
• Angular momentum conservation for dynamical black holes
• A Reformulation of the Hoop Conjecture
• Fundamental properties and applications of quasi-local black hole horizons
• Isolated horizons in higher-dimensional Einstein-Gauss-Bonnet gravity
• Trapping Horizons as inner boundary conditions for black hole spacetimes
• Supersymmetric isolated horizons
• Two physical characteristics of numerical apparent horizons
• Extending the isolated horizon phase space to string-inspired gravity models