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

Space-Time Structure of Loop Quantum Black Hole

In this paper we have improved the semiclassical analysis of loop quantum black hole (LQBH) in the conservative approach of constant polymeric parameter. In particular we have focused our attention on the space-time structure. We have introduced a very simple modification of the spherically symmetric Hamiltonian constraint in its holonomic version. The new quantum constraint reduces to the classical constraint when the polymeric parameter goes to zero.Using this modification we have obtained a large class of semiclassical solutions parametrized by a generic function of the polymeric parameter. We have found that only a particular choice of this function reproduces the black hole solution with the correct asymptotic flat limit. In r=0 the semiclassical metric is regular and the Kretschmann invariant has a maximum peaked in L-Planck. The radial position of the pick does not depend on the black hole mass and the polymeric parameter. The semiclassical solution is very similar to the Reissner-Nordstrom metric. We have constructed the Carter-Penrose diagrams explicitly, giving a causal description of the space-time and its maximal extension. The LQBH metric interpolates between two asymptotically flat regions, the r to infinity region and the r to 0 region. We have studied the thermodynamics of the semiclassical solution. The temperature, entropy and the evaporation process are regular and could be defined independently from the polymeric parameter. We have studied the particular metric when the polymeric parameter goes towards to zero. This metric is regular in r=0 and has only one event horizon in r = 2m. The Kretschmann invariant maximum depends only on L-Planck. The polymeric parameter does not play any role in the black hole singularity resolution. The thermodynamics is the same.Comment: 17 pages, 19 figure

Physical boundary state for the quantum tetrahedron

We consider stability under evolution as a criterion to select a physical boundary state for the spinfoam formalism. As an example, we apply it to the simplest spinfoam defined by a single quantum tetrahedron and solve the associated eigenvalue problem at leading order in the large spin limit. We show that this fixes uniquely the free parameters entering the boundary state. Remarkably, the state obtained this way gives a correlation between edges which runs at leading order with the inverse distance between the edges, in agreement with the linearized continuum theory. Finally, we give an argument why this correlator represents the propagation of a pure gauge, consistently with the absence of physical degrees of freedom in 3d general relativity.Comment: 20 pages, 6 figure

A semiclassical tetrahedron

We construct a macroscopic semiclassical state state for a quantum tetrahedron. The expectation values of the geometrical operators representing the volume, areas and dihedral angles are peaked around assigned classical values, with vanishing relative uncertainties.Comment: 10 pages; v2 revised versio

Numerical indications on the semiclassical limit of the flipped vertex

We introduce a technique for testing the semiclassical limit of a quantum gravity vertex amplitude. The technique is based on the propagation of a semiclassical wave packet. We apply this technique to the newly introduced "flipped" vertex in loop quantum gravity, in order to test the intertwiner dependence of the vertex. Under some drastic simplifications, we find very preliminary, but surprisingly good numerical evidence for the correct classical limit.Comment: 4 pages, 8 figure

Area-angle variables for general relativity

We introduce a modified Regge calculus for general relativity on a triangulated four dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These variables satisfy constraints which are local in the triangulation. We expect the formulation to have applications to classical discrete gravity and non-perturbative approaches to quantum gravity.Comment: 7 pages, 1 figure. v2 small changes to match published versio

On the perturbative expansion of a quantum field theory around a topological sector

The idea of treating general relativistic theories in a perturbative expansion around a topological theory has been recently put forward in the quantum gravity literature. Here we investigate the viability of this idea, by applying it to conventional Yang--Mills theory on flat spacetime. We find that the expansion around the topological theory coincides with the usual expansion around the abelian theory, though the equivalence is non-trivial. In this context, the technique appears therefore to be viable, but not to bring particularly new insights. Some implications for gravity are discussed.Comment: 7 page

Loop quantum gravity: the first twenty five years

This is a review paper invited by the journal "Classical ad Quantum Gravity" for a "Cluster Issue" on approaches to quantum gravity. I give a synthetic presentation of loop gravity. I spell-out the aims of the theory and compare the results obtained with the initial hopes that motivated the early interest in this research direction. I give my own perspective on the status of the program and attempt of a critical evaluation of its successes and limits.Comment: 24 pages, 3 figure

Graviton propagator in loop quantum gravity

We compute some components of the graviton propagator in loop quantum gravity, using the spinfoam formalism, up to some second order terms in the expansion parameter.Comment: 41 pages, 6 figure

Laplacians on discrete and quantum geometries

We extend discrete calculus for arbitrary ($p$-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries.Comment: 43 pages, 2 multiple figures. v2: discussion improved, references added, minor typos correcte