43 research outputs found
Non-commutative holonomies in 2+1 LQG and Kauffman's brackets
We investigate the canonical quantization of 2+1 gravity with {\Lambda} > 0
in the canonical framework of LQG. A natural regularization of the constraints
of 2+1 gravity can be defined in terms of the holonomies of A\pm = A \PM
\surd{\Lambda}e, where the SU(2) connection A and the triad field e are the
conjugated variables of the theory. As a first step towards the quantization of
these constraints we study the canonical quantization of the holonomy of the
connection A_{\lambda} = A + {\lambda}e acting on spin network links of the
kinematical Hilbert space of LQG. We provide an explicit construction of the
quantum holonomy operator, exhibiting a close relationship between the action
of the quantum holonomy at a crossing and Kauffman's q-deformed crossing
identity. The crucial difference is that the result is completely described in
terms of standard SU(2) spin network states.Comment: 4 pages; Proceedings of Loops'11, Madrid, to appear in Journal of
Physics: Conference Series (JPCS
Gravity from symmetry: duality and impulsive waves
We show that we can derive the asymptotic Einsteinâs equations that arises at order 1/r in asymptotically flat gravity purely from symmetry considerations. This is achieved by studying the transformation properties of functionals of the metric and the stress-energy tensor under the action of the Weyl BMS group, a recently introduced asymptotic symmetry group that includes arbitrary diffeomorphisms and local conformal transformations of the metric on the 2-sphere. Our derivation, which encompasses the inclusion of matter sources, leads to the identification of covariant observables that provide a definition of conserved charges parametrizing the non-radiative corner phase space. These observables, related to the Weyl scalars, reveal a duality symmetry and a spin-2 generator which allow us to recast the asymptotic evolution equations in a simple and elegant form as conservation equations for a null fluid living at null infinity. Finally we identify non-linear gravitational impulse waves that describe transitions among gravitational vacua and are non-perturbative solutions of the asymptotic Einsteinâs equations. This provides a new picture of quantization of the asymptotic phase space, where gravitational vacua are representations of the asymptotic symmetry group and impulsive waves are encoded in their couplings
Black hole quantum atmosphere for freely falling observers
We analyze Hawking radiation as perceived by a freely-falling observer and try to draw an inference about the region of origin of the Hawking quanta. To do so, first we calculate the energy density from the stress energy tensor, as perceived by a freely-falling observer. Then we compare this with the energy density computed from an effective temperature functional which depends on the state of the observer. The two ways of computing these quantities show a mismatch at the light ring outside the black hole horizon. To better understand this ambiguity, we show that even taking into account the (minor) breakdown of the adiabatic evolution of the temperature functional which has a peak in the same region of the mismatch, is not enough to remove it. We argue that the appearance of this discrepancy can be traced back to the process of particle creation by showing how the WentzelâKramersâBrillouin approximation for the field modes breaks down between the light ring at 3M and 4M, with a peak at r=3.3M exactly where the energy density mismatch is maximized. We hence conclude that these facts strongly support a scenario where the Hawking flux does originate from a âquantum atmosphereâ located well outside the black hole horizon. © 2019 The Author
Higher spin dynamics in gravity and w1+â celestial symmetries
In this paper we extract from a large-r expansion of the vacuum Einstein's equations a dynamical system governing the time evolution of an infinity of higher-spin charges. Upon integration, we evaluate the canonical action of these charges on the gravity phase space. The truncation of this action to quadratic order and the associated charge conservation laws yield an infinite tower of soft theorems. We show that the canonical action of the higher spin charges on gravitons in a conformal primary basis, as well as conformally soft gravitons reproduces the higher spin celestial symmetries derived from the operator product expansion. Finally, we give direct evidence that these charges form a canonical representation of a w1+â loop algebra on the gravitational phase space
Entropy in the Classical and Quantum Polymer Black Hole Models
We investigate the entropy counting for black hole horizons in loop quantum
gravity (LQG). We argue that the space of 3d closed polyhedra is the classical
counterpart of the space of SU(2) intertwiners at the quantum level. Then
computing the entropy for the boundary horizon amounts to calculating the
density of polyhedra or the number of intertwiners at fixed total area.
Following the previous work arXiv:1011.5628, we dub these the classical and
quantum polymer models for isolated horizons in LQG. We provide exact
micro-canonical calculations for both models and we show that the classical
counting of polyhedra accounts for most of the features of the intertwiner
counting (leading order entropy and log-correction), thus providing us with a
simpler model to further investigate correlations and dynamics. To illustrate
this, we also produce an exact formula for the dimension of the intertwiner
space as a density of "almost-closed polyhedra".Comment: 24 page
Canonical quantization of non-commutative holonomies in 2+1 loop quantum gravity
In this work we investigate the canonical quantization of 2+1 gravity with
cosmological constant in the canonical framework of loop quantum
gravity. The unconstrained phase space of gravity in 2+1 dimensions is
coordinatized by an SU(2) connection and the canonically conjugate triad
field . A natural regularization of the constraints of 2+1 gravity can be
defined in terms of the holonomies of . As a first step
towards the quantization of these constraints we study the canonical
quantization of the holonomy of the connection on the
kinematical Hilbert space of loop quantum gravity. The holonomy operator
associated to a given path acts non trivially on spin network links that are
transversal to the path (a crossing). We provide an explicit construction of
the quantum holonomy operator. In particular, we exhibit a close relationship
between the action of the quantum holonomy at a crossing and Kauffman's
q-deformed crossing identity. The crucial difference is that (being an operator
acting on the kinematical Hilbert space of LQG) the result is completely
described in terms of standard SU(2) spin network states (in contrast to
q-deformed spin networks in Kauffman's identity). We discuss the possible
implications of our result.Comment: 19 pages, references added. Published versio
Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
A dual formulation of group field theories, obtained by a Fourier transform
mapping functions on a group to functions on its Lie algebra, has been proposed
recently. In the case of the Ooguri model for SO(4) BF theory, the variables of
the dual field variables are thus so(4) bivectors, which have a direct
interpretation as the discrete B variables. Here we study a modification of the
model by means of a constraint operator implementing the simplicity of the
bivectors, in such a way that projected fields describe metric tetrahedra. This
involves a extension of the usual GFT framework, where boundary operators are
labelled by projected spin network states. By construction, the Feynman
amplitudes are simplicial path integrals for constrained BF theory. We show
that the spin foam formulation of these amplitudes corresponds to a variant of
the Barrett-Crane model for quantum gravity. We then re-examin the arguments
against the Barrett-Crane model(s), in light of our construction.Comment: revtex, 24 page
A Note on the Symmetry Reduction of SU(2) on Horizons of Various Topologies
It is known that the SU(2) degrees of freedom manifest in the description of
the gravitational field in loop quantum gravity are generally reduced to U(1)
degrees of freedom on an isolated horizon. General relativity also allows
black holes with planar, toroidal, or higher genus topology for their horizons.
These solutions also meet the criteria for an isolated horizon, save for the
topological criterion, which is not crucial. We discuss the relevant
corresponding symmetry reduction for black holes of various topologies (genus 0
and ) here and discuss its ramifications to black hole entropy within
the loop quantum gravity paradigm. Quantities relevant to the horizon theory
are calculated explicitly using a generalized ansatz for the connection and
densitized triad, as well as utilizing a general metric admitting hyperbolic
sub-spaces. In all scenarios, the internal symmetry may be reduced to
combinations of U(1).Comment: 13 pages, two figures. Version 2 has several references updated and
added, as well as some minor changes to the text. Accepted for publication in
Class. Quant. Gra
The SU(2) black hole entropy revisited
We study the state-counting problem that arises in the SU(2) black hole entropy calculation in loop quantum gravity. More precisely, we compute the leading term and the logarithmic correction of both the spherically symmetric and the distorted SU( 2) black holes. Contrary to what has been done in previous works, we have to take into account "quantum corrections" in our framework in the sense that the level k of the Chern-Simons theory which describes the black hole is finite and not sent to infinity. Therefore, the new results presented here allow for the computation of the entropy in models where the quantum group corrections are important
Geometric temperature and entropy of quantum isolated horizons
By reintroducing Lorentz invariance in canonical loop quantum gravity, we define a geometrical notion of temperature for quantum isolated horizons. This is done by demanding that the horizon state satisfying the boundary conditions be a Kubo-Martin-Schwinger state. The exact formula for the temperature can be derived by imposing the reality conditions in the form of the linear simplicity constraints for an imaginary Barbero-Immirzi parameter. Thus, our analysis reveals the connection between the analytic continuation to the Ashtekar self-dual variables and the thermality of the horizon. The horizon thermal equilibrium state can then be used to compute both the entanglement and the Boltzmann entropies. We show that the two provide the same finite answer, which allows us to recover the Bekenstein-Hawking formula in the semiclassical limit. In this way, we shed new light on the microscopic origin of black hole entropy by revealing the equivalence between the near-horizon degrees of freedom entanglement proposal and the state-counting interpretation. The connection with the Connes-Rovelli thermal time proposal for a general relativistic statistical mechanics is worked out. \ua9 2014 American Physical Society