1,019 research outputs found
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.Comment: 5 pages, 5 figure
Higher-order Cartan symmetries in k-symplectic field theory
For k-symplectic Hamiltonian field theories, we study infinitesimal
transformations generated by certain kinds of vector fields which are not
Noether symmetries, but which allow us to obtain conservation laws by means of
a suitable generalization of the Noether theorem.Comment: 11 page
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Mass Inflation in the Loop Black Hole
In classical general relativity the Cauchy horizon within a two-horizon black
hole is unstable via a phenomenon known as mass inflation, in which the mass
parameter (and the spacetime curvature) of the black hole diverges at the
Cauchy horizon. Here we study this effect for loop black holes -- quantum
gravitationally corrected black holes from loop quantum gravity -- whose
construction alleviates the singularity present in their classical
counterparts. We use a simplified model of mass inflation, which makes use of
the generalized DTR relation, to conclude that the Cauchy horizon of loop black
holes indeed results in a curvature singularity similar to that found in
classical black holes. The DTR relation is of particular utility in the loop
black hole because it does not directly rely upon Einstein's field equations.
We elucidate some of the interesting and counterintuitive properties of the
loop black hole, and corroborate our results using an alternate model of mass
inflation due to Ori.Comment: Latex 20 pages, 7 figure
Effective Polymer Dynamics of D-Dimensional Black Hole Interiors
We consider two different effective polymerization schemes applied to
D-dimensional, spherically symmetric black hole interiors. It is shown that
polymerization of the generalized area variable alone leads to a complete,
regular, single-horizon spacetime in which the classical singularity is
replaced by a bounce. The bounce radius is independent of rescalings of the
homogeneous internal coordinate, but does depend on the arbitrary fiducial cell
size. The model is therefore necessarily incomplete. It nonetheless has many
interesting features: After the bounce, the interior region asymptotes to an
infinitely expanding Kantowski-Sachs spacetime. If the solution is analytically
continued across the horizon, the black hole exterior exhibits asymptotically
vanishing quantum-corrections due to the polymerization. In all spacetime
dimensions except four, the fall-off is too slow to guarantee invariance under
Poincare transformations in the exterior asymptotic region. Hence the
four-dimensional solution stands out as the only example which satisfies the
criteria for asymptotic flatness. In this case it is possible to calculate the
quantum-corrected temperature and entropy. We also show that polymerization of
both phase space variables, the area and the conformal mode of the metric,
generically leads to a multiple horizon solution which is reminiscent of
polymerized mini-superspace models of spherically symmetric black holes in Loop
Quantum Gravity.Comment: 14 pages, 4 figures. Added discussion about the dependency on
auxiliary structures. Matches with the published versio
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.Comment: 16 pages, 2 figure
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
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 naturally implies a Generalized Uncertainty Principle
with the linear form . We also
demonstrate a natural dimensional reduction feature, in that the gravitational
radius and thermodynamics of sub-Planckian objects resemble that of -D
gravity. The temperature of sub-Planckian black holes scales as rather than
but the evaporation of those smaller than 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
Loop quantum black hole
In this paper we consider the Kantowski-Sachs space-time in Ashtekar
variables and the quantization of this space-time starting from the complete
loop quantum gravity theory. The Kanthowski-Sachs space-time coincides with the
Schwarzschild black hole solution inside the horizon. By studying this model we
can obtain information about the black hole singularity and about the dynamics
across the point r=0. We studied this space-time in ADM variables in two
previous papers where we showed that the classical black hole singularity
disappears in quantum theory. In this work we study the same model in Ashtekar
variables and we obtain a regular space-time inside the horizon region and that
the dynamics can be extend further the classical singularity.Comment: 12 pages, latex. We introduce and we calculate the spectrum of the
operator 1/|E
Background independence in a nutshell
We study how physical information can be extracted from a background
independent quantum system. We use an extremely simple `minimalist' system that
models a finite region of 3d euclidean quantum spacetime with a single
equilateral tetrahedron. We show that the physical information can be expressed
as a boundary amplitude. We illustrate how the notions of "evolution" in a
boundary proper-time and "vacuum" can be extracted from the background
independent dynamics.Comment: 19 pages, 19 figure
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