Self-completeness and spontaneous dimensional reduction

A viable quantum theory of gravity is one of the biggest challenges facing physicists. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity -- spontaneous dimensional reduction and self-completeness. The former suggests the spacetime background at the Planck scale may be effectively two-dimensional, while the latter implies a condition of maximal compression of matter by the formation of an event horizon for Planckian scattering. We generalize such a result to an arbitrary number of dimensions, and show that gravity in higher than four dimensions remains self-complete, but in lower dimensions it is not. In such a way we established an "exclusive disjunction" or "exclusive or" (XOR) between the occurrence of self-completeness and dimensional reduction, with the goal of actually reducing the unknowns for the scenario of the physics at the Planck scale. Potential phenomenological implications of this result are considered by studying the case of a two-dimensional dilaton gravity model resulting from dimensional reduction of Einstein gravity.Comment: 12 pages, 3 figures; v3: final version in press on Eur. Phys. J. Plu

Diagnosing numerical Cherenkov instabilities in relativistic plasma simulations based on general meshes

Numerical Cherenkov radiation (NCR) or instability is a detrimental effect frequently found in electromagnetic particle-in-cell (EM-PIC) simulations involving relativistic plasma beams. NCR is caused by spurious coupling between electromagnetic-field modes and multiple beam resonances. This coupling may result from the slow down of poorly-resolved waves due to numerical (grid) dispersion and from aliasing mechanisms. NCR has been studied in the past for finite-difference-based EM-PIC algorithms on regular (structured) meshes with rectangular elements. In this work, we extend the analysis of NCR to finite-element-based EM-PIC algorithms implemented on unstructured meshes. The influence of different mesh element shapes and mesh layouts on NCR is studied. Analytic predictions are compared against results from finite-element-based EM-PIC simulations of relativistic plasma beams on various mesh types.Comment: 31 pages, 20 figure

Practice-Focused, Constructivist Grounded Theory Methodology In Higher Education Leadership Research

A growing body of education research considers practices, however there is less focus on a methodology that enables practical analysis of practices. Use of practice theory is growing, particularly in work and organisational studies, but practice focused studies more frequently address theoretical than methodological agenda. This chapter proposes a practice-focused, constructivist grounded theory methodology as one approach which can address this gap. After first considering the ways in which, separately and in combination, practice-theory and constructivist grounded theory can support higher education leadership and management research, the chapter considers implementation of this methodology by drawing on a study into the practice of authority in higher education leadership. It concludes by considering some implications for the ways in which practices can be understood and the affordances and limitations of this methodology.Peer reviewe

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

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

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

H-theorem for classical matter around a black hole

We propose a classical solution for the kinetic description of matter falling into a black hole, which permits to evaluate both the kinetic entropy and the entropy production rate of classical infalling matter at the event horizon. The formulation is based on a relativistic kinetic description for classical particles in the presence of an event horizon. An H-theorem is established which holds for arbitrary models of black holes and is valid also in the presence of contracting event horizons

The Hidden Quantum Groups Symmetry of Super-renormalizable Gravity

In this paper we consider the relation between the super-renormalizable theories of quantum gravity (SRQG) studied in [arXiv:1110.5249v2, arXiv:1202.0008] and an underlying non-commutativity of spacetime. For one particular super-renormalizable theory we show that at linear level (quadratic in the Lagrangian) the propagator of the theory is the same we obtain starting from a theory of gravity endowed with {\theta}-Poincar\'e quantum groups of symmetry. Such a theory is over the so called {\theta}-Minkowski non-commuative spacetime. We shed new light on this link and show that among the theories considered in [arXiv:1110.5249v2, arXiv:1202.0008], there exist only one non-local and Lorentz invariant super-renormalizable theory of quantum gravity that can be described in terms of a quantum group symmetry structure. We also emphasize contact with pre-existent works in the literature and discuss preservation of the equivalence principle in our framework.Comment: 10 page

Sub-Planckian black holes and the Generalized Uncertainty Principle

The Black Hole Uncertainty Principle correspondence suggests that there could exist black holes with mass beneath the Planck scale but radius of order the Compton scale rather than Schwarzschild scale. We present a modified, self-dual Schwarzschild-like metric that reproduces desirable aspects of a variety of disparate models in the sub-Planckian limit, while remaining Schwarzschild in the large mass limit. The self-dual nature of this solution under $M \leftrightarrow M^{-1}$ naturally implies a Generalized Uncertainty Principle with the linear form $\Delta x \sim \frac{1}{\Delta p} + \Delta p$. We also demonstrate a natural dimensional reduction feature, in that the gravitational radius and thermodynamics of sub-Planckian objects resemble that of $(1+1)$-D gravity. The temperature of sub-Planckian black holes scales as $M$ rather than $M^{-1}$ but the evaporation of those smaller than $10^{-36}$g is suppressed by the cosmic background radiation. This suggests that relics of this mass could provide the dark matter.Comment: 12 pages, 9 figures, version published in J. High En. Phy

Hawking emission from quantum gravity black holes

We address the issue of modelling quantum gravity effects in the evaporation of higher dimensional black holes in order to go beyond the usual semi-classical approximation. After reviewing the existing six families of quantum gravity corrected black hole geometries, we focus our work on non-commutative geometry inspired black holes, which encode model independent characteristics, are unaffected by the quantum back reaction and have an analytical form compact enough for numerical simulations. We consider the higher dimensional, spherically symmetric case and we proceed with a complete analysis of the brane/bulk emission for scalar fields. The key feature which makes the evaporation of non-commutative black holes so peculiar is the possibility of having a maximum temperature. Contrary to what happens with classical Schwarzschild black holes, the emission is dominated by low frequency field modes on the brane. This is a distinctive and potentially testable signature which might disclose further features about the nature of quantum gravity.Comment: 36 pages, 18 figures, v2: updated reference list, minor corrections, version matching that published on JHE