Holographic screens in ultraviolet self-complete quantum gravity

In this paper we study the geometry and the thermodynamics of a holographic screen in the framework of the ultraviolet self-complete quantum gravity. To achieve this goal we construct a new static, neutral, non-rotating black hole metric, whose outer (event) horizon coincides with the surface of the screen. The space-time admits an extremal configuration corresponding to the minimal holographic screen and having both mass and radius equalling the Planck units. We identify this object as the space-time fundamental building block, whose interior is physically unaccessible and cannot be probed even during the Hawking evaporation terminal phase. In agreement with the holographic principle, relevant processes take place on the screen surface. The area quantization leads to a discrete mass spectrum. An analysis of the entropy shows that the minimal holographic screen can store only one byte of information while in the thermodynamic limit the area law is corrected by a logarithmic term.Comment: 18 pages, 4 figures; v2 additional references; v3 shortened version in press as invited contribution to "Black hole Physics'', special issue of Advances of High Energy Physics edited by X. Zeng, C. Corda and D. Che

Black holes production in self-complete quantum gravity

A regular black hole model, which has been proposed by Hayward, is reconsidered in the framework of higher dimensional TeV unification and self-complete quantum gravity scenario (Dvali, Spallucci). We point out the "quantum" nature of these objects and compute their cross section production by taking into account the key role played by the existence of a "minimal length" l_0. We show as the threshold energy is related to l_0. We recover, in the high energy limit, the standard "black-disk" form of the cross section, while it vanishes, below threshold, faster than any power of the invariant mass-energy \sqrt{-s}.Comment: 12 pages; 3 figures; accepted for publication in PL

Thermodynamical phases of a regular SAdS black hole

This paper studies the thermodynamical stability of regular BHs in AdS5 background. We investigate off-shell free energy of the system as a function of temperature for different values of a "coupling constant" L=4 theta/l^2, where the cosmological constant is Lambda = -3/l^2 and \sqrt{theta} is a "minimal length". The parameter L admits a critical value, L_{inf}=0.2, corresponding to the appearance of an inflexion point in the Hawking temperature. In the weak-coupling regime L < L_{inf}, there are first order phase transitions at different temperatures. Unlike the Hawking-Page case, at temperature 0\le T \le T_{min} the ground state is populated by "cold" near-extremal BHs instead of a pure radiation. On the other hand, for L \g L_{inf} only large, thermodynamically stable, BHs exist.Comment: 12 pages; 6 Figures; accepted for publication in Int. J. Mod. Phys.

Zero-point length, extra-dimensions and string T-duality

In this paper, we are going to put in a single consistent framework apparently unrelated pieces of information, i.e. zero-point length, extra-dimensions, string T-duality. More in details we are going to introduce a modified Kaluza-Klein theory interpolating between (high-energy) string theory and (low-energy) quantum field theory. In our model zero-point length is a four dimensional ``virtual memory'' of compact extra-dimensions length scale. Such a scale turns out to be determined by T-duality inherited from the underlying fundamental string theory. From a low energy perspective short distance infinities are cut off by a minimal length which is proportional to the square root of the string slope, i.e. \sqrt{\alpha^\prime}. Thus, we provide a ``bridge'' between the ultra-relativistic string domain and the low energy arena of point-particle quantum field theory.Comment: 28 pages, Latex, no figures; two references adde

Un-spectral dimension and quantum spacetime phases

In this Letter, we propose a new scenario emerging from the conjectured presence of a minimal length $\ell$ in the spacetime fabric, on the one side, and the existence of a new scale invariant, continuous mass spectrum, of un-particles on the other side. We introduce the concept of \textit{un-spectral dimension} $\mathbb{D}_U$ of a $d$-dimensional, euclidean (quantum) spacetime, as the spectral dimension measured by an "un-particle" probe. We find a general expression for the un-spectral dimension $\mathbb{D}_U$ labelling different spacetime phases: a semi-classical phase, where ordinary spectral dimension gets contribution from the scaling dimension $d_U$ of the un-particle probe ; a critical "Planckian phase", where four-dimensional spacetime can be effectively considered two-dimensional when $d_U=1$; a "Trans-Planckian phase", which is accessible to un-particle probes only, where spacetime as we currently understand it looses its physical meaning.Comment: 5 pages, 1 figure, version matching that published by Physics Letters

Maxwell's equal area law and the Hawking-Page phase transition

In this paper we study the phases of a Schwarzschild black hole in the Anti deSitter background geometry. Exploiting fluid/gravity duality we construct the Maxwell equal area isotherm T=T* in the temperature-entropy plane, in order to eliminate negative heat capacity black hole configurations. The construction we present here is reminiscent of the isobar cut in the pressure-volume plane which eliminates un-physical part of the Van der Walls curves below the critical temperature. Our construction also modifies the Hawking-Page phase transition. Stable black holes are formed at the temperature T > T*, while pure radiation persists for T< T*. T* turns out to be below the standard Hawking-Page temperature and there are no unstable black holes as in the usual scenario. Also, we show that in order to reproduce the correct black hole entropy S=A/4, one has to write a black hole equation of state, i.e. P=P(V), in terms of the geometrical volume V=4\pi r^3/3.Comment: 15 pages, 4 Figures. Accepted for publication in Journal of Gravit