# Isolated horizons: The classical phase space

@article{Ashtekar1999IsolatedHT, title={Isolated horizons: The classical phase space}, author={Abhay Ashtekar and Alejandro Corichi and Kirill Krasnov}, journal={Advances in Theoretical and Mathematical Physics}, year={1999}, volume={3}, pages={419-478} }

A Hamiltonian framework is introduced to encompass non-rotating (but possibly charged) black holes that are “isolated” near future time-like infinity or for a finite time interval. The underlying space-times need not admit a stationary Killing field even in a neighborhood of the horizon; rather, the physical assumption is that neither matter fields nor gravitational radiation fall across the portion of the horizon under consideration. A precise notion of non-rotating isolated horizons is…

## 203 Citations

Supersymmetric isolated horizons

- Physics
- 2008

We construct a covariant phase space for rotating weakly isolated horizons in Einstein–Maxwell–Chern–Simons theory in all (odd) D ⩾ 5 dimensions. In particular, we show that horizons on the…

Weakly Isolated Horizons: $3+1$ decomposition and canonical formulations in self-dual variables

- Physics
- 2022

The notion of Isolated Horizons has played an important role in gravitational physics, being useful from the characterization of the endpoint of black hole mergers to (quantum) black hole entropy. In…

Classical and Quantum Physics of Isolated Horizons: A Brief Overview

- Physics
- 2000

The arena normally used in black holes thermodynamics was recently generalized to incorporate a broad class of physically interesting situations. The key idea is to replace the notion of stationary…

Weakly Isolated horizons: first order actions and gauge symmetries

- Physics
- 2016

The notion of Isolated Horizons has played an important role in gravitational physics, being useful from the characterization of the endpoint of black hole mergers to (quantum) black hole entropy.…

New variables for classical and quantum gravity in all dimensions: V. Isolated horizon boundary degrees of freedom

- Physics
- 2013

In this paper, we generalize the treatment of isolated horizons in loop quantum gravity, resulting in a Chern–Simons theory on the boundary in the four-dimensional case, to non-distorted isolated…

Isolated horizons: Hamiltonian evolution and the first law

- Physics
- 2000

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…

Static Isolated Horizons: SU(2) Invariant Phase Space, Quantization, and Black Hole Entropy

- PhysicsEntropy
- 2011

It is argued how this difficulty could be avoided by a simple enlargement of the field content at the horizon that restores diffeomorphism invariance, and a quantization of the horizon degrees of freedom is proposed.

Mechanics of isolated horizons

- Physics
- 1999

A set of boundary conditions defining an undistorted, non-rotating isolated horizon are specified in general relativity. A spacetime representing a black hole which is itself in equilibrium but whose…

Interface of General Relativity, Quantum Physics and Statistical Mechanics: Some Recent Developments

- PhysicsAnnalen der Physik
- 2000

The arena normally used in black holes thermodynamics was recently generalized to incorporate a broad class of physically interesting situations. The key idea is to replace the notion of stationary…

LETTER TO THE EDITOR: Isolated horizons: a generalization of black hole mechanics

- Physics
- 1999

A set of boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A spacetime representing a black hole which itself is in equilibrium but whose exterior…

## References

SHOWING 1-10 OF 58 REFERENCES

Mechanics of isolated horizons

- Physics
- 1999

A set of boundary conditions defining an undistorted, non-rotating isolated horizon are specified in general relativity. A spacetime representing a black hole which is itself in equilibrium but whose…

LETTER TO THE EDITOR: Isolated horizons: a generalization of black hole mechanics

- Physics
- 1999

A set of boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A spacetime representing a black hole which itself is in equilibrium but whose exterior…

Quantum geometry of isolated horizons and black hole entropy

- Physics
- 2000

Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting…

Spatial infinity as a boundary of spacetime

- Mathematics
- 1992

A definition of asymptotic flatness at spatial infinity is given by imposing conditions at a time-like boundary of a completed 4-manifold. The resulting framework is similar to the Penrose…

Action Integrals and Partition Functions in Quantum Gravity

- Physics
- 1977

One can evaluate the action for a gravitational field on a section of the complexified spacetime which avoids the singularities. In this manner we obtain finite, purely imaginary values for the…

Linking topological quantum field theory and nonperturbative quantum gravity

- Mathematics
- 1995

Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory in which the…

General laws of black-hole dynamics.

- GeologyPhysical review. D, Particles and fields
- 1994

The future outer trapping horizon provides the definition of a black hole, and general ``laws of black-hole dynamics'' derived.

Spin coefficient form of the new laws of black hole dynamics

- Mathematics
- 1994

General laws of black hole dynamics, some of which are analogous to the laws of thermodynamics, have recently been found for a general definition of a black hole in terms of a future outer trapping…

Black hole entropy is Noether charge.

- MathematicsPhysical review. D, Particles and fields
- 1993

The results show that the validity of the "second law" of black hole mechanics in dynamical evolution from an initially stationary black hole to a final stationary state is equivalent to the positivity of a total Noether flux, and thus may be intimately related to the positive energy properties of the theory.