## Quantum Geometry of Isolated Horizons and Black Hole Entropy (1999)

Venue: | Adv. Theor. Math. Phys |

Citations: | 45 - 3 self |

### BibTeX

@ARTICLE{Ashtekar99quantumgeometry,

author = {Abhay Ashtekar and John C. Baez and Kirill Krasnov},

title = {Quantum Geometry of Isolated Horizons and Black Hole Entropy},

journal = {Adv. Theor. Math. Phys},

year = {1999},

volume = {4},

pages = {0005126}

}

### OpenURL

### Abstract

Using the classical Hamiltonian framework of [1] as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting non-rotating isolated horizons as inner boundaries. The emphasis is on the quantum geometry of the horizon. Polymer excitations of the bulk quantum geometry pierce the horizon endowing it with area. The intrinsic geometry of the horizon is then described by the quantum Chern-Simons theory of a U(1) connection on a punctured 2-sphere, the horizon. Subtle mathematical features of the quantum Chern-Simons theory turn out to be important for the existence of a coherent quantum theory of the horizon geometry. Heuristically, the intrinsic geometry is at everywhere except at the punctures. The distributional curvature of the U(1) connection at the punctures gives rise to quantized decit angles which account for the overall curvature. For macroscopic black holes, the logarithm of the number of t...