This writeup is a compilation of the predictions for the forthcoming Heavy Ion Program at the Large Hadron Collider, as presented at the CERN Theory Institute ‘Heavy Ion Collisions at the LHC—Last Call for Predictions’, held from 14th May to 10th June 2007.
Scale dependence at the level of the effective action is a generic result of quantum field theory. Allowing for scale dependence of the gravitational couplings leads to a generalization of the corresponding field equations. In this work, those equations are solved by imposing the "null energy condition" in three-dimensional space time with stationary spherical symmetry. The constants of integration are given in terms of the classical BTZ parameters plus one additional constant, that parametrizes the strength of the scale dependence. The properties such as asymptotics, horizon structure, and thermodynamics are discussed. It is found that the black hole entropy shows a remarkable transition from the usual "area law" to an "area × radius" law.PACS numbers: 04.60., 04.70. I. INTRODUCTIONGravity in (2 + 1) dimensions is a vibrant field of research. This is in part due to the fact that the absence of propagating degrees of freedom makes things simpler than in (3 + 1) dimensions, in particular when dealing with the challenge of formulating a quantization of this theory. Another important feature of gravity in (2 + 1) dimensions is the deep connection to Chern-Simons theory [1][2][3]. This by itself makes the black hole solution [4,5] found by Bañados, Teitelboim, and Zanelli (BTZ) an extremely interesting research object, which has been generalised in many directions. An additional component that motivates the research on black holes in three dimensions is their prominent role in the context of the AdS/CFT correspondence [6][7][8][9].Despite of some progress, the consistent formulation of quantum gravity remains an open task which is attacked in many different ways [10-26] (for a review see [27]). Even though many approaches to quantum gravity are very different, most of them have the common feature that the resulting effective action of gravity acquires a scale dependence. This means that the couplings appearing in the quantum-effective action (such as Newtons coupling G 0 , or the cosmological term Λ 0 ) become scale dependent quantities (G 0 → G k , Λ 0 → Λ k ). There is quite some evidence that this scaling behavior is in agreement with Weinberg's Asymptotic Safety program [28][29][30][31][32][33][34][35]. In particular, the effective action and running couplings in three dimensions have been studied in [36,37]. In any case, scale dependent couplings can be expected to produce differences to classical general relativity, such as modifications of classical black hole backgrounds .In this paper the possible effects of scale dependence on the black hole in three dimensional gravity will be investigated in the light of the effective action approach. We will use the scale-field method applied to the Einstein-Hilbert truncation, which allows to derive generalized Einstein equations for the case of scale dependent couplings [59][60][61][62]. The theoretical uncertainty concerning the functional form of the scale dependence of G k and Λ k will be avoided. Instead, the most general stationary spherically symmetric solution w...
We study the quantum modifications of classical, spherically symmetric Schwarzschild (Anti-) de Sitter black holes within Quantum Einstein Gravity. The quantum effects are incorporated through the running coupling constants G k and Λ k , computed within the exact renormalization group approach, and a common scalesetting procedure. We find that, in contrast to common intuition, it is actually the cosmological constant that determines the short-distance structure of the RG-improved black hole: in the asymptotic UV the structure of the quantum solutions is universal and given by the classical Schwarzschild-de Sitter solution, entailing a self-similarity between the classical and quantum regime. As a consequence asymptotically safe black holes evaporate completely and no Planck-size remnants are formed. Moreover, the thermodynamic entropy of the critical Nariai-black hole is shown to agree with the microstate count based on the effective average action, suggesting that the entropy originates from quantum fluctuations around the mean-field geometry.
Black holes are probably among the most fascinating objects populating our universe. Their characteristic features found within general relativity, encompassing spacetime singularities, event horizons, and black hole thermodynamics, provide a rich testing ground for quantum gravity ideas. We review the status of black holes within a particular proposal for quantum gravity, Weinberg's asymptotic safety program. Starting from a brief survey of the effective average action and scale setting procedures, an improved quantum picture of the black hole is developed. The Schwarzschild black hole and its generalizations including angular momenta, higher-derivative corrections and the implications of extra dimensions are discussed in detail. In addition, the quantum singularity emerging for the inclusion of a cosmological constant is elucidated and linked to the phenomenon of a dynamical dimensional reduction of spacetime.
In the present work we study the scale-dependence of polytropic non-charged black holes in (3+1)-dimensional space-times assuming a cosmological constant. We allow for scale-dependence of the gravitational and cosmological couplings, and we solve the corresponding generalized field equations imposing the null energy condition. Besides, some properties, such as horizon structure and thermodynamics, are discussed in detail.
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