Special Issue "Entropy in Quantum Gravity"

Guest Editor
Dr. Remo Garattini
Faculty of Engineering, University of Bergamo, Viale Marconi 5, 24044 Dalmine (Bergamo), Italy
E-Mail:
Interests: quantum gravity; quantum cosmology; quantum field theory

Dear Colleagues,

Almost thirty years after the introduction of the famous Bekenstein–Hawking formula [Bekenstein, J.D. Phys. Rev. 1973, D 7, 949. Hawking, S.W. Comm. Math. Phys. 1975, 43, 199.], relating the entropy of a black hole and its area, the thermodynamics of such objects still attracts research in this direction. One reason is due to the lack of a Quantum Gravity theory that should be able to explain black hole physics. Another reason comes from the fact that Hawking radiation develops modes of arbitrarily high frequency near the horizon. It is clear that the subject of studying Entropy in Quantum Gravity is far to be exhausted. This special section would focus on different contributions and approaches by some of the leading researchers in this field.

- scope: to provide a set of essays to illustrate the different approaches in different areas of Quantum Gravity that try to explain the connection between entropy and geometry.

- motivation: the motivation for this issue comes out of a discussion in different workshops and conferences concerning quantum gravity. These different discussions illustrated needs for clarification and interpretation of the different view angles of Entropy-Area relation and Entropy in the context of Quantum Gravity. The invited and contributed essays of this special section would help to clarify this important theoretical foundation.

Remo Garattini, Ph. D.
Guest Editor

Submission

All manuscripts should be submitted to entropy@mdpi.org with a copy to the Guest Editor. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed Open Access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this Open Access journal is 1000 CHF per accepted paper.

• entropy
• quantum gravity
• quantum field theory
• quantum cosmology

Type of Paper: Article
Title: Black Hole Horizons and Thermodynamics: A Quantum Approach
Authors: Valter Moretti¹ and Nicola Pinamonti²
Affiliations: ¹ Via Rodolfo Belenzani, 12, 38100 Trento, Trento, Italy; ‎E-Mail: moretti@science.unitn.it
² University of Hamburg, Edmund-Siemers-Allee 1, 20146 Rotherbaum, Hamburg, Germany
Abstract: We focus on quantization of the metric of a black hole restricted to the Killing horizon with universal radius $r_0$.
The metric is represented in a suitable manner after imposing spherical symmetry and, after restriction to the Killing horizon, it is quantized employing chiral currents. Two ``components of the metric'' are in fact quantized: one behaves as an affine scalar fields under changes of coordinates and the other is a proper scalar field.
The symplectic group acts on both fields as subgroup of diffeomorphisms of the horizon and this action, in some cases depending on the choice of the vacuum state, can be implemented by means of a unitary group. If the reference state of the scalar field is not a vacuum state but a coherent state, spontaneous breaking of conformal symmetry arises and the state contains a Bose-Einstein condensate. In this case the order parameter fixes the actual size of the black hole with respect to $r_0$. This state together with that associated with the affine scalar when restricted in a half horizon (the future boundary of the external region of the black hole) is recognized to be thermal (KMS) with respect to Schwarzschild Killing time restricted to the horizon. The value of the order parameter individuates Hawking temperature as well. As a result it is found that the densities, energy and entropy of this state scales like the mass and the entropy of the black hole and they coincide with them provided the universal parameter $r_0$ is fixed appropriately not depending on the size of the actual black hole.

Type of Paper: Article
Title: The Microcanonical Description of (Micro) Black Holes
Authors: R. Casadio and B. Harms
Affiliation: Dipartimento di Fisica, via Irnerio 46, 40126 Bologna, Italy; E-Mail: Roberto.Casadio@bo.infn.it
Abstract: The microcanonical ensemble is the proper ensemble to describe black holes which are not in thermodynamic equilibrium, such as radiating black holes. This choice of ensemble eliminates the problems, e.g. negative specific heat and loss of unitarity, encountered when the canonical ensemble is used. In this review we present an overview of the weaknesses of the standard thermodynamic description of black holes and show how the microcanonical approach can provide a consistent description of black holes and their Hawking radiation at all energy scales. Our approach is based on viewing the horizon area as yielding the ensemble density at fixed system energy. We then compare the decay rates of black holes in the two different pictures. Our description is particularly relevant for the analysis of micro-black holes whose existence is predicted in models with extra-spatial dimensions.