black hole horizons and thermodynamics a quantum approach黑洞热力学视野,一个量子的方法.pdf

Entropy 2010, 12, 1833-1854; doi:10.3390/ OPEN ACCESS entropy ISSN 1099-4300 /journal/entropy Article Black Hole Horizons and Thermodynamics: A Quantum Approach Valter Moretti 1,⋆ and Nicola Pinamonti 2 1 ` Dipartimento di Matematica, Universita di Trento and Istituto Nazionale di Fisica Nucleare–Gruppo Collegato di Trento, via Sommarive 14 I-38050 Povo (TN), Italy 2 ` Dipartimento di Matematica, Universita di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, I-00133 Roma, Italy; E-Mail: pinamont@mat.uniroma2.it ⋆ Author to whom correspondence should be addressed; E-Mail: moretti@science.unitn.it. Received: 24 June 2010; in revised form: 20 July 2010 / Accepted: 21 July 2010 / Published: 23 July 2010 Abstract: We focus on quantization of the metric of a black hole restricted to the Killing horizon with universal radius r . After imposing spherical symmetry and after restriction to 0 the Killing horizon, the metric is quantized employing the chiral currents formalism. Two “components of the metric” are indeed quantized: The former behaves as an affine scalar field under changes of coordinates, the latter is instead a proper scalar field. The action of the symplectic group on both fields is realized in terms of certain horizon diffeomorphisms. Depending on the choice of the vacuum state, such a representation is unitary. If the reference state of the scal