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

@article{Perez2011StaticIH,
  title={Static Isolated Horizons: SU(2) Invariant Phase Space, Quantization, and Black Hole Entropy},
  author={Alejandro Perez and Daniele Pranzetti},
  journal={Entropy},
  year={2011},
  volume={13},
  pages={744-777}
}
We study the classical field theoretical formulation of static generic isolated horizons in a manifestly SU(2) invariant formulation. We show that the usual classical description requires revision in the non-static case due to the breaking of diffeomorphism invariance at the horizon leading to the non-conservation of the usual pre-symplectic structure. We argue how this difficulty could be avoided by a simple enlargement of the field content at the horizon that restores diffeomorphism… 

Figures from this paper

Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
We review the black hole entropy calculation in the framework of Loop Quantum Gravity based on the quasi-local definition of a black hole encoded in the isolated horizon formalism. We show, by means
New variables for classical and quantum gravity in all dimensions: V. Isolated horizon boundary degrees of freedom
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
Note on SU(2) isolated horizon
  • A. Majhi
  • Physics
    Classical and Quantum Gravity
  • 2020
We point out that the symplectic structure, written in terms of the Sen–Ashtekar–Immirzi–Barbero variables, of a spacetime admitting an isolated horizon as the inner boundary, involves a positive
Anyonic statistics and large horizon diffeomorphisms for loop quantum gravity black holes
We investigate the role played by large diffeomorphisms of quantum Isolated Horizons for the statistics of LQG Black Holes by means of their relation to the braid group. To this aim the symmetries of
M ay 2 01 3 Black hole entropy from KMS-states of quantum isolated horizons
By reintroducing Lorentz invariance via a complex connection formulation in canonical loop quantum gravity, we define a geometrical notion of temperature for quantum isolated horizons. Upon
‘Quantum hairs’ and entropy of the quantum isolated horizon from Chern–Simons theory
We articulate the fact that the loop quantum gravity (LQG) description of the quantum macrostates of black hole horizons, modeled as quantum isolated horizons (QIHs), is completely characterized in
Semiclassical analysis of black holes in loop quantum gravity: Modeling Hawking radiation with volume fluctuations
We introduce the notion of fluid approximation of a quantum spherical black hole in the context of loop quantum gravity. In this limit, the microstates of the black hole are intertwiners between
Asymptotically de Sitter universe inside a Schwarzschild black hole
Extending our previous analysis, we study the interior of a Schwarzschild black hole derived from a partial gauge fixing of the full Loop Quantum Gravity Hilbert space, this time including the
...
...

References

SHOWING 1-10 OF 71 REFERENCES
Isolated horizons: The classical phase space
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
Black hole entropy and SU(2) Chern-Simons theory.
TLDR
This work shows that this boundary condition given on a null surface representing the event horizon can be treated in a manifestly SU(2) invariant manner and settles previous controversies concerning the counting of states.
Generic isolated horizons in loop quantum gravity
Isolated horizons model equilibrium states of classical black holes. A detailed quantization, starting from a classical phase space restricted to spherically symmetric horizons, exists in the
Entropy of Isolated Horizons revisited
The decade-old formulation of the isolated horizon classically and within loop quantum gravity, and the extraction of the microcanonical entropy of such a horizon from this formulation, is reviewed,
Black hole entropy from the SU(2)-invariant formulation of type I isolated horizons
A detailed analysis of the spherically symmetric isolated horizon system is performed in terms of the connection formulation of general relativity. The system is shown to admit a manifestly SU(2)
Quantum geometry of isolated horizons and black hole entropy
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
Entropy from Conformal Field Theory at Killing Horizons
On a manifold with a boundary, the constraint algebra of general relativity may acquire a central extension, which can be computed using covariant phase space techniques. When the boundary is a
Algebraic approach to quantum black holes: Logarithmic corrections to black hole entropy
The algebraic approach to black hole quantization requires the horizon area eigenvalues to be equally spaced. As shown previously, for a neutral non-rotating black hole, such eigenvalues must be
Isolated horizons: Hamiltonian evolution and the first law
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
...
...