A model of radiating black hole in noncommutative geometry

The phenomenology of a radiating Schwarzschild black hole is analyzed in a noncommutative spacetime. It is shown that noncommutativity does not depend on the intensity of the curvature. Thus we legitimately introduce noncommutativity in the weak field limit by a coordinate coherent state approach. The new interesting results are the following: i) the existence of a minimal non-zero mass to which black hole can shrink; ii) a finite maximum temperature that the black hole can reach before cooling down to absolute zero; iii) the absence of any curvature singularity. The proposed scenario offers a possible solution to conventional difficulties when describing terminal phase of black hole evaporation.Comment: 10 pages, 4 figure

Minimal Scales from an Extended Hilbert Space

We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our commutators do not depend on positions and momenta and we provide an extension of the coordinate coherent state approach to Noncommutative Geometry. We explore, as toy model, the corresponding quantum field theory in a (2+1)-dimensional spacetime. Then we investigate the more realistic case of a (3+1)-dimensional spacetime, foliated into noncommutative planes. As a result, we obtain propagators, which are finite in the ultraviolet as well as the infrared regime.Comment: 16 pages, version which matches that published on CQ

Finite axionic electrodynamics from a new noncommutative approach

Using the gauge-invariant but path-dependent variables formalism, we compute the static quantum potential for noncommutative axionic electrodynamics (or axionic electrodynamics in the presence of a minimal length). Accordingly, we obtain an ultraviolet finite static potential which is the sum of a Yukawa-type and a linear potential, leading to the confinement of static charges. Interestingly, it should be noted that this calculation involves no theta expansion at all. The present result makes manifest the key role played by the new quantum of length in our analysis.Comment: 14 pages, 2 figures, final version to appear in J.Phys.A, added comments, reference list update

TeV Mini Black Hole Decay at Future Colliders

It is generally believed that mini black holes decay by emitting elementary particles with a black body energy spectrum. The original calculation lead to the conclusion that about the 90% of the black hole mass is radiated away in the form of photons, neutrinos and light leptons, mainly electrons and muons. With the advent of String Theory, such a scenario must be updated by including new effects coming from the stringy nature of particles and interactions.By taking for granted that black holes can be produced in hadronic collisions, then their decay must take into account that: (i) we live in a D3-Brane embedded into an higher dimensional bulk spacetime; (ii) fundamental interactions, including gravity, are unified at TeV energy scale. Thus, the formal description of the Hawking radiation mechanism has to be extended to the case of more than four spacetime dimensions and include the presence of D-branes. Furthermore, unification of fundamental interactions at an energy scale many order of magnitude lower than the Planck energy implies that any kind of fundamental particle, not only leptons, is expected to be emitted. A detailed understanding of the new scenario is instrumental for optimal tuning of detectors at future colliders, where, hopefully, this exciting new physics will be tested. In this article we review higher dimensional black hole decay, considering not only the emission of particles according to Hawking mechanism, but also their near horizon QED/QCD interactions. The ultimate motivation is to build up a phenomenologically reliable scenario, allowing a clear experimental signature of the event.Comment: 22 pages, 9 figures, 4 tables; ``quick review'' for Class. and Quantum Gra

Tunneling of massive and charged particles from noncommutative Reissner-Nordstr\"{o}m black hole

Massive charged and uncharged particles tunneling from commutative Reissner-Nordstrom black hole horizon has been studied with details in literature. Here, by adopting the coherent state picture of spacetime noncommutativity, we study tunneling of massive and charged particles from a noncommutative inspired Reissner-Nordstrom black hole horizon. We show that Hawking radiation in this case is not purely thermal and there are correlations between emitted modes. These correlations may provide a solution to the information loss problem. We also study thermodynamics of noncommutative horizon in this setup.Comment: 10 pages, 2 figure

Gravitational Collapse of the Shells with the Smeared Gravitational Source in Noncommutative Geometry

We study the formation of the (noncommutative) Schwarzschild black hole from collapsing shell {of the} generalized matters containing polytropic and Chaplygin gas. We show that this collapsing shell depending on various parameters forms either a black hole or a naked singular shell with the help of the pressure.Furthermore, by considering the smeared gravitational sources, we investigate the noncommutative black holes formation. Though this mild noncommutative correction of matters cannot ultimately resolve the emergence of the naked singularity, we show that in some parameter region the collapsing shell evolves to a noncommutative black hole before becoming a naked singular shell.Comment: 16 pages, LateX, 9 figures, Title changed in this published versio

Spinning Loop Black Holes

In this paper we construct four Kerr-like spacetimes starting from the loop black hole Schwarzschild solutions (LBH) and applying the Newman-Janis transformation. In previous papers the Schwarzschild LBH was obtained replacing the Ashtekar connection with holonomies on a particular graph in a minisuperspace approximation which describes the black hole interior. Starting from this solution, we use a Newman-Janis transformation and we specialize to two different and natural complexifications inspired from the complexifications of the Schwarzschild and Reissner-Nordstrom metrics. We show explicitly that the space-times obtained in this way are singularity free and thus there are no naked singularities. We show that the transformation move, if any, the causality violating regions of the Kerr metric far from r=0. We study the space-time structure with particular attention to the horizons shape. We conclude the paper with a discussion on a regular Reissner-Nordstrom black hole derived from the Schwarzschild LBH and then applying again the Newmann-Janis transformation.Comment: 18 pages, 18 figure

The Hawking-Page crossover in noncommutative anti-deSitter space

We study the problem of a Schwarzschild-anti-deSitter black hole in a noncommutative geometry framework, thought to be an effective description of quantum-gravitational spacetime. As a first step we derive the noncommutative geometry inspired Schwarzschild-anti-deSitter solution. After studying the horizon structure, we find that the curvature singularity is smeared out by the noncommutative fluctuations. On the thermodynamics side, we show that the black hole temperature, instead of a divergent behavior at small scales, admits a maximum value. This fact implies an extension of the Hawking-Page transition into a van der Waals-like phase diagram, with a critical point at a critical cosmological constant size in Plank units and a smooth crossover thereafter. We speculate that, in the gauge-string dictionary, this corresponds to the confinement "critical point" in number of colors at finite number of flavors, a highly non-trivial parameter that can be determined through lattice simulations.Comment: 24 pages, 6 figure, 1 table, version matching that published on JHE

Noncommutative Geometry Inspired Rotating Black Hole in Three Dimensions

We find a new rotating black hole in three-dimensional anti-de Sitter space using an anisotropic perfect fluid inspired by the noncommutative black hole. We deduce the thermodynamical quantities of this black hole and compare them with those of a rotating BTZ solution.Comment: 7 page

Minimum length effects in black hole physics

We review the main consequences of the possible existence of a minimum measurable length, of the order of the Planck scale, on quantum effects occurring in black hole physics. In particular, we focus on the ensuing minimum mass for black holes and how modified dispersion relations affect the Hawking decay, both in four space-time dimensions and in models with extra spatial dimensions. In the latter case, we briefly discuss possible phenomenological signatures.Comment: 29 pages, 12 figures. To be published in "Quantum Aspects of Black Holes", ed. X. Calmet (Springer, 2014