Isolated horizons: Hamiltonian evolution and the first law

By Abhay Ashtekar, Stephen Fairhurst, B. Krishnan. 2000

310 citations recorded by the source corpus.

A framework was recently introduced to generalize black hole mechanics by replacing stationary event horizons with isolated horizons. That framework is significantly extended. The extension is nontrivial in that not only do the boundary conditions now allow the horizon to be distorted and rotating, but also the subsequent analysis is based on several new ingredients. Specifically, although the overall strategy is closely related to that in the previous work, the dynamical variables, the action principle and the Hamiltonian framework are all quite different. More importantly, in the nonrotating case, the first law is shown to arise as a necessary and sufficient condition for the existence of a consistent Hamiltonian evolution. Somewhat surprisingly, this consistency condition in turn leads to new predictions even for static black holes. To complement the previous work, the entire discussion is presented in terms of tetrads and associated (real) Lorentz connections.

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

View Paper: https://www.semanticscholar.org/paper/72b3fd883e89f99810c26ab5506e55477d7a3795

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Citations in the corpus

FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY (2005, background): “This is the so-called isolated horizon classically defined by Ashtekar et al (see R f.[15] for a precise definition).”
Mechanics of rotating isolated horizons (2001, background): “Thus, this paper is a continuation of [4] and completes the task of deriving the black hole mechanics of all isolated horizons of direct physical interest.”
Black hole entropy from the SU(2)-invariant formulation of type I isolated horizons (2010, background): “The general treatment and derivation of the first law can be found in [19, 21].”
Multipole moments of isolated horizons (2004, methodology): “The isolated horizon definition extracts from the notion of the Killing horizon just that ‘tiny’ part which turns out to be essential for black hole mechanics [9, 11] and, more generally, to capture the notion that the horizon is in equilibrium, allowing for dynamical processes and radiation in the ”
A 3+1 perspective on null hypersurfaces and isolated horizons (2005, methodology): “Instead of using a formal presentation (see [15,12,107]) we introduce the basic concepts by illustrating them with examples extracted from the isolated horizon literature, always in absence of matter.”
Geometry of Generic Isolated Horizons (2001, methodology): “Let as apply the above results of the last subsection to non-rotating horizons, i.e., horizons satisfying ω̃a =̂ 0.”
Asymptotics with a positive cosmological constant: I. Basic framework (2014, background): “However, the first law of black hole thermodynamics restricts the freedom to change the normalization as one moves from one space–time to another [44].”
Introduction to isolated horizons in numerical relativity (2002, methodology): “In the regime when the black hole is isolated in an otherwise dynamical spacetime, such a framework now exists in the form of isolated horizons [9, 10, 11, 12, 13].”