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Leonardo Modesto

Publications and source records attributed to Leonardo Modesto.

At least 127 records · Page 7Linked to original sources
arXiv2010

Charged rotating noncommutative black holes

In this paper we complete the program of the noncomutative geometry inspired black holes, providing the richest possible solution, endowed with mass, charge and angular momentum. After providing a prescription for employing the Newman-Janis algorithm in the case of nonvanishing stress tensors, we find regular axisymmetric charged black holes in the presence of a minimal length. We study also the new thermodynamics and we determine the corresponding higher-dimensional solutions. As a conclusion we make some consideration about possible applications.

gr-qc↗
arXiv2010

Stability of self-dual black holes

We study the stability properties of the Cauchy horizon for two different self-dual black hole solutions obtained in a model inspired by Loop Quantum Gravity. The self-dual spacetimes depend on a free dimensionless parameter called a polymeric parameter P. For the first metric the Cauchy horizon is stable for supermassive black holes only if this parameter is sufficiently small. For small black holes, however the stability is easily implemented. The second metric analyzed is not only self-dual but also "form-invariant" under the transformation r -> r*^2/r and r* = 2 m P. We find that this symmetry protects the Cauchy horizon for any value of the polymeric parameter.

gr-qc↗
arXiv2010

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.

gr-qc↗
arXiv2010

Spectral dimension of a quantum universe

In this paper, we calculate in a transparent way the spectral dimension of a quantum spacetime, considering a diffusion process propagating on a fluctuating manifold. To describe the erratic path of the diffusion, we implement a minimal length by averaging the graininess of the quantum manifold in the flat space case. As a result we obtain that, for large diffusion times, the quantum spacetime behaves like a smooth differential manifold of discrete dimension. On the other hand, for smaller diffusion times, the spacetime looks like a fractal surface with a reduced effective dimension. For the specific case in which the diffusion time has the size of the minimal length, the spacetime turns out to have a spectral dimension equal to 2, suggesting a possible renormalizable character of gravity in this regime. For smaller diffusion times, the spectral dimension approaches zero, making any physical interpretation less reliable in this extreme regime. We extend our result to the presence of a background field and curvature. We show that in this case the spectral dimension has a more complicated relation with the diffusion time, and conclusions about the renormalizable character of gravity become less straightforward with respect to what we found with the flat space analysis.

hep-th↗
arXiv2010

Entropic corrections to Newton's law

It has been known for some time that there is a deep connection between thermodynamics and gravity, with perhaps the most dramatic implication that the Einstein equations can be viewed as a thermodynamic equation of state. Recently Verlinde has proposed a model for gravity with a simple statistical mechanical interpretation that is applicable in the non-relatvistic regime. After critically analyzing the construction, we present a strong consistency check of the model. Specifically, we consider two well-motivated corrections to the area-entropy relation, the log correction and the volume correction, and follow Verlinde's construction to derive corrections to Newton's law of gravitation. We show that the deviations from Newton's law stemming from the log correction have the same form as the lowest order quantum effects of perturbative quantum gravity, and the deviations stemming from the volume correction have the same form as some modified Newtonian gravity models designed to explain the anomalous galactic rotation curves.

hep-th↗
arXiv2010

A model for non-singular black hole collapse and evaporation

We study the formation of a black hole and its subsequent evaporation in a model employing a minisuperspace approach to loop quantum gravity. In previous work the static solution was obtained and shown to be singularity-free. Here, we examine the more realistic dynamical case by generalizing the static case with help of the Vaidya metric. We track the formation and evolution of trapped surfaces during collapse and evaporation and examine the buildup of quantum gravitationally caused stress-energy preventing the formation of a singularity.

gr-qc↗
arXiv2009

Fractal Space-Time from Spin-Foams

In this paper we perform the calculation of the spectral dimension of spacetime in 4d quantum gravity using the Barrett-Crane (BC) spinfoam model. We realize this considering a very simple decomposition of the 4d spacetime already used in the graviton propagator calculation and we introduce a boundary state which selects a classical geometry on the boundary. We obtain that the spectral dimension of the spacetime runs from $\approx 2$ to 4, across a $\approx 1.5$ phase, when the energy of a probe scalar field decreases from high $E \lesssim E_P/25$ to low energy. The spectral dimension at the Planck scale $E \approx E_P$ depends on the areas spectrum used in the calculation. For three different spectra $l_P^2 \sqrt{j(j+1)}$, $l_P^2 (2 j+1)$ and $l_P^2 j$ we find respectively dimension $\approx 2.31$, 2.45 and 2.08.

gr-qc↗
arXiv2009

In, Through and Beyond the Planck Scale

In this paper we have recalled the semiclassical metric obtained from a classical analysis of the loop quantum black hole (LQBH). We show that the regular Reissner-Nordström-like metric is self-dual in the sense of T-duality: the form of the metric is invariant under the exchange r -> a0/r where a0 is proportional to the minimum area in LQG. Of particular interest, the symmetry imposes that if an observer at infinity sees a black hole of mass m an observer in the other asymptotic infinity beyond the horizon (near r=0) sees a dual mass proportional to m_P^2/m. We then show that small LQBHs are stable and could be a component of dark matter. Ultra-light LQBHs created shortly after the Big Bang would now have a mass of approximately 10^(-5) m_P and emit radiation with a typical energy of about 10^(13) - 10^(14) eV but they would also emit cosmic rays of much higher energies, albeit few of them. If these small LQBHs form a majority of the dark matter of the Milky Way's Halo, the production rate of ultra-high-energy-cosmic-rays (UHECR) by these ultra light black holes would be compatible with the observed rate of the Auger detector.

hep-th↗
arXiv2009

Self-dual Black Holes in LQG: Theory and Phenomenology

In this paper we have recalled the semiclassical metric obtained from a classical analysis of the loop quantum black hole (LQBH). We show that the regular Reissner-Nordstrom-like metric is self-dual in the sense of T-duality: the form of the metric obtained in Loop quantum Gravity (LQG) is invariant under the exchange "r <-> a0/r" where "a0" is proportional to the minimum area in LQG and "r" is the standard Schwarzschild radial coordinate at asymptotic infinity. Of particular interest, the symmetry imposes that if an observer at "r" close to infinity sees a black hole of mass "m" an observer in the other asymptotic infinity beyond the horizon (at "r" close to "0") sees a dual mass "mp/m" ("mp" is the Planck mass). We then show that small LQBH are stable and could be a component of dark matter. Ultra-light LQBHs created shortly after the Big Bang would now have a mass of approximately "10^(-5) mp" and emit radiation with a typical energy of about 10^(13) - 10^(14) eV but they would also emit cosmic rays of much higher energies, albeit few of them. If these small LQBHs form a majority of the dark matter of the Milky Way's Halo, the production rate of ultra-high-energy-cosmic-rays (UHECR) by these ultra light black holes would be compatible with the observed rate of the Auger detector.

hep-th↗
arXiv2009

Black hole interior from loop quantum gravity

In this paper we calculate modifications to the Schwarzschild solution by using a semiclassical analysis of loop quantum black hole. We obtain a metric inside the event horizon that coincides with the Schwarzschild solution near the horizon but that is substantially different at the Planck scale. In particular we obtain a bounce of the two-sphere for a minimum value of the radius and that it is possible to have another event horizon close to the r=0 point.

gr-qc↗
arXiv2009

Fractal Dimension in 3d Spin-Foams

In this paper we perform the calculation of the spectral dimension of the space-time in 3d quantum gravity using the dynamics of the Ponzano-Regge vertex (PR) and its quantum group generalization (Turaev-Viro model (TV)). We realize this considering a very simple decomposition of the 3d space-time and introducing a boundary state which selects a classical geometry on the boundary. We obtain that the spectral dimension of the space-time runs from 2 to 3, across a 1.5 phase, when the energy of a probe scalar field decreases from high to low energy. For the TV model the spectral dimension at hight energy increase with the value of the cosmological constant. At low energy the presence of the cosmological constant does not change the spectral dimension.

gr-qc↗
arXiv2009

Fractal Quantum Space-Time

In this paper we calculated the spectral dimension of loop quantum gravity (LQG) using the scaling property of the area operator spectrum on spin-network states and using the scaling property of the volume and length operators on Gaussian states. We obtained that the spectral dimension of the spatial section runs from 1.5 to 3, and under particular assumptions from 2 to 3 across a 1.5 phase when the energy of a probe scalar field decreases from high to low energy in a fictitious time T. We calculated also the spectral dimension of space-time using the scaling of the area spectrum operator calculated on spin-foam models. The main result is that the effective dimension is 2 at the Planck scale and 4 at low energy. This result is consistent with two other approaches to non perturbative quantum gravity: "causal dynamical triangulation" and "asymptotically safe quantum gravity". We studied the scaling properties of all the possible curvature invariants and we have shown that the singularity problem seems to be solved in the covariant formulation of quantum gravity in terms of spin-foam models. For a particular form of the scaling (or for a particular area operator spectrum) all the curvature invariants are regular also in the Trans-Planckian regime.

gr-qc↗
arXiv2008

Fractal Structure of Loop Quantum Gravity

In this paper we have calculated the spectral dimension of loop quantum gravity (LQG) using simple arguments coming from the area spectrum at different length scales. We have obtained that the spectral dimension of the spatial section runs from 2 to 3, across a 1.5 phase, when the energy of a probe scalar field decrees from high to low energy. We have calculated the spectral dimension of the space-time also using results from spin-foam models, obtaining a 2-dimensional effective manifold at hight energy. Our result is consistent with other two approach to non perturbative quantum gravity: causal dynamical triangulation and asymptotic safety quantum gravity.

gr-qc↗
arXiv2008

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.

gr-qc↗
arXiv2007

The perturbative Regge-calculus regime of Loop Quantum Gravity

The relation between Loop Quantum Gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In this paper we study a semiclassical regime of Loop Quantum Gravity and show that it admits an effective description in terms of perturbative area-Regge-calculus. The regime of interest is identified by a class of states given by superpositions of four-valent spin networks, peaked on large spins. As a probe of the dynamics in this regime, we compute explicitly two- and three-area correlation functions at the vertex amplitude level. We find that they match with the ones computed perturbatively in area-Regge-calculus with a single 4-simplex, once a specific perturbative action and measure have been chosen in the Regge-calculus path integral. Correlations of other geometric operators and the existence of this regime for other models for the dynamics are briefly discussed.

gr-qc↗
arXiv2006

Evaporating loop quantum black hole

In this paper we obtain the black hole metric from a semiclassical analysis of loop quantum black hole. Our solution and the Schwarzschild one tend to match well at large distances from Planck region. In r=0 the semiclassical metric is regular and singularity free in contrast to the classical one. By using the new metric we calculate the Hawking temperature and the entropy. For the entropy we obtain the logarithmic correction to the classical area law. Finally we study the mass evaporation process and we show the mass and temperature tend to zero at infinitive time.

gr-qc↗
arXiv2006

Gravitational collapse in loop quantum gravity

In this paper we study the gravitational collapse in loop quantum gravity. We consider the space-time region inside the Schwarzschild black hole event horizon and we divide this region in two parts, the first one where the matter (dust matter) is localized and the other (outside) where the metric is Kantowski-Sachs type. We calculate the state solving Hamiltonian constraint and we obtain a set of three difference equations that give a regular and natural evolution beyond the classical singularity point in "r=0" localized.

gr-qc↗