Isolated and Dynamical Horizons and Their Applications

By Abhay Ashtekar, B. Krishnan. Living Reviews in Relativity, 2004

734 citations recorded by the source corpus.

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modelled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity, and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity, suggested a phenomenological model for hairy black holes, provided novel techniques to extract physics from numerical simulations, and led to new laws governing the dynamics of black holes in exact general relativity.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c57f6dcc7b2eb31afbcd02a61097e86d8b37d9db

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Citations in the corpus

Loop quantum gravity: an outside view (2005, background): “The LQG explanation, on the other hand, succeeds in implementing the condition for isolated horizons [51] in the quantum theory, and works for ordinary (Schwarzschild and Kerr) black holes, but requires a ‘fit’ for the Barbero Immirzi parameter to get the prefactor right.”
Introduction to loop quantum gravity and spin foams (2004, background): “An example of three different graphs on which the Wilson loop function (74) can be defined.”
Asymptotic perfect fluid dynamics as a consequence of AdS/CFT correspondence (2005, background): “discussions in the context of dynamical horizons in general relativity [25]).”
Loop quantization of the Schwarzschild interior revisited (2015, background): “For instance, as part of the definition of an isolated horizon [19], one has to specify the precise values of all the multipole moments of the horizon.”
Present status of the Penrose inequality (2009, neutral): “The interested reader is referred to [9], [7], [4], [1], [140], [8], [98], [69], [166], [2], [75], [3] and references therein.”
Transition rate of the Unruh–DeWitt detector in curved spacetime (2007, background): “For example, a detector that is falling freely into a static black hole in a Boulware-type vacuum [29] would be expected to have a divergent response at the horizon, in analogy with the Rindler vacuum analysis in section 5, but might any thermal characteristics survive in the response of a detector ”
Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes (2007, background): “See [9] for a review of some of these issues.”
Black-hole entropy from quantum geometry (2004, background): “This idea gave rise to a new quasi-local theory of black-hole in equilibrium interesting also from purely classical point of view [12].”
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”
Phenomenological aspects of black holes beyond general relativity (2018, background): “On the other hand, trapping horizons are known to be spacelike for standard accreting matter [135, 136].”
A 3+1 perspective on null hypersurfaces and isolated horizons (2005, background): “These source multipoles present a vast domain of applications [14,18] ranging from the description of the motion of a black hole inside a strong external gravitational field, the study of the effects on the black hole induced by a companion or the invariant comparison at sufficiently late times of t”
Some uniqueness results for dynamical horizons (2005, methodology): “, admit DHs H which are smoothly joined onto IHs ∆ in the future [10].”
The Spin-Foam Approach to Quantum Gravity (2012, background): “34 An interesting example, where this is strictly realized, is the midi-superspace formulation of black holes in the context of LQG known as the isolated-horizon formulation (see [31] for a review).”
A Holographic View on Physics out of Equilibrium (2010, background): “62 For a good review of various notions of quasilocal horizons, see [226, 227].”
The fluid/gravity correspondence: a new perspective on the membrane paradigm (2010, positive): “Alternately, several (quasi)local notions of a black hole have been proposed, such as the so-called dynamical horizon [62, 63], which however are spacelike surfaces inside the event horizon, and therefore do not admit the standard notion of evolution.”
Local Fluid Dynamical Entropy from Gravity (2008, background): “These two conditions single out a 5 dimensional submanifold of non-negative divergence entropy currents in the 7 dimensional space (6.1) of candidate Weyl covariant entropy currents.”