Dynamical Horizons and their Properties

By Abhay Ashtekar, B. Krishnan. 2003

351 citations recorded by the source corpus.

A detailed description of how black holes grow in full, non-linear general relativity is presented. The starting point is the notion of dynamical horizons. Expressions of fluxes of energy and angular momentum carried by gravitational waves across these horizons are obtained. Fluxes are local and the energy flux is positive. Change in the horizon area is related to these fluxes. A notion of angular momentum and energy is associated with cross-sections of the horizon and balance equations, analogous to those obtained by Bondi and Sachs at null infinity, are derived. These in turn lead to generalizations of the first and second laws of black hole mechanics. The relation between dynamical horizons and their asymptotic states —the isolated horizons— is discussed briefly. The framework has potential applications to numerical, mathematical, astrophysical and quantum general relativity.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d0bdcb1c2f5eadba471ede8cd70215f3f9b9d58f

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Citations in the corpus

Isolated and Dynamical Horizons and Their Applications (2004, background): “First, there exist expressions for mass and angular momentum of dynamical and isolated horizons which enable one to monitor dynamical processes occurring in the simulations [28] and extract properties of the final equilibrium state [13, 72].”
Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes (2007, methodology): “We call a 3-surface foliated by MOTS a marginally outer trapped tube (MOTT) [15, 16]; an alternative terminology adopted in [1] is “trapping horizon”, c.”
Gravity and the Thermodynamics of Horizons (2003, background): “It is more difficult to extend the results to general, time dependent , horizons (for a discussion of issues involved in providing a general definition of horizon, see e.g., Ashtekar and Krishnan (2003); Date (2001)).”
Spherically symmetric quantum geometry: Hamiltonian constraint (2005, background): “The isolated or dynamical horizon framework [94, 95, 96, 97, 98, 99] provides an ideal setting for an analysis at the classical and quantum levels.”
Inspiral, merger and ring-down of equal-mass black-hole binaries (2006, neutral): “Brown & York[5] or Ashtekar & Krishnan[2] S = − 1 8π ∮”
Gravity and the thermodynamics of horizons (2005, neutral): “, [29,30]).”
A 3+1 perspective on null hypersurfaces and isolated horizons (2005, background): “Secondly, a systematic attempt to provide a quasi-local description2 of black holes has been initiated in the recent years by Hayward [93,94] (concept of future trapping horizons) and Ashtekar and collaborators [10–17] — see Refs.”
Black hole evaporation: a paradigm (2005, background): “For the massless scalar field under consideration, during and for a long time after the collapse, it would be spacelike [25, 26] and thus constitute a dynamical horizon [27, 28].”
Nonlinear fluid dynamics from gravity (2007, background): “The language of dynamical horizons(30) [51] may well prove to be the appropriate framework for such a discussion.”
A covariant holographic entanglement entropy proposal (2007, result): “A dynamical horizon is defined to be a smooth, co-dimension one spacelike submanifold of the spacetime, which can be foliated by a family of closed spacelike surfaces, such that the leaves of the foliation have one null expansion vanishing and the other null expansion being strictly negative [55, 47”
Some uniqueness results for dynamical horizons (2005, methodology): “It and DH have provided extremely useful structures for numerical relativity, black hole thermodynamics, quantum gravity and mathematical physics of hairy black holes [3, 4, 6, 8, 9].”