arXiv subjects

Karim Noui

Publications and source records attributed to Karim Noui.

At least 55 records · Page 3Linked to original sources

arXiv2016

Semi-classical analysis of black holes in Loop Quantum Gravity: Modelling Hawking radiation with volume fluctuations

We introduce the notion of fluid approximation of a quantum spherical black hole in the context of Loop Quantum Gravity. In this limit, the microstates of the black hole are intertwiners between "large" representations $s_i$ which typically scale as $s_i \sim \sqrt{a_H}$ where $a_H$ denotes the area of the horizon in Planck units. The punctures with large colors are, for the black hole horizon, similar to what are the fluid parcels for a classical fluid. We dub them puncels. Hence, in the fluid limit, the horizon is composed by puncels which are themselves interpreted as composed (in the sense of the tensor product) by a large number of more fundamental intertwiners. We study the spectrum of the euclidean volume acting on puncels and we compute its quantum fluctuations. Then, we propose an interpretation of black holes radiation based on the properties of the quantum fluctuations of the euclidean volume operator. We estimate a typical temperature of the black hole and we show that it scales as the Hawking temperature.

gr-qc↗

arXiv2016

Healthy degenerate theories with higher derivatives

In the context of classical mechanics, we study the conditions under which higher-order derivative theories can evade the so-called Ostrogradsky instability. More precisely, we consider general Lagrangians with second order time derivatives, of the form $L(\ddotϕ^a,\dotϕ^a,ϕ^a;\dot q^i,q^i)$ with $a = 1,\cdots, n$ and $i = 1,\cdots, m$. For $n=1$, assuming that the $q^i$'s form a nondegenerate subsystem, we confirm that the degeneracy of the kinetic matrix eliminates the Ostrogradsky instability. The degeneracy implies, in the Hamiltonian formulation of the theory, the existence of a primary constraint, which generates a secondary constraint, thus eliminating the Ostrogradsky ghost. For $n>1$, we show that, in addition to the degeneracy of the kinetic matrix, one needs to impose extra conditions to ensure the presence of a sufficient number of secondary constraints that can eliminate all the Ostrogradsky ghosts. When these conditions that ensure the disappearance of the Ostrogradsky instability are satisfied, we show that the Euler-Lagrange equations, which involve a priori higher order derivatives, can be reduced to a second order system.

hep-th↗

arXiv2016

Analytic continuation of the rotating black hole state counting

In loop quantum gravity, a spherical black hole can be described in terms of a Chern-Simons theory on a punctured 2-sphere. The sphere represents the horizon. The punctures are the edges of spin-networks in the bulk which cross the horizon and carry quanta of area. One can generalize this construction and model a rotating black hole by adding an extra puncture colored with the angular momentum J in the 2-sphere. We compute the entropy of rotating black holes in this model and study its semi-classical limit. After performing an analytic continuation which sends the Barbero-Immirzi parameter to +/- i, we show that the leading order term in the semi-classical expansion of the entropy reproduces the Bekenstein-Hawking law independently of the value of J.

gr-qc↗

arXiv2016

Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering "degenerate" Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom. In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field. We thus obtain a classification of all degenerate theories within this class of scalar-tensor theories. The quartic Horndeski Lagrangian and its extension beyond Horndeski belong to these degenerate cases. We also identify new families of scalar-tensor theories with the intriguing property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian.

gr-qc↗

arXiv2016

Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations

We consider all degenerate scalar-tensor theories that depend quadratically on second order derivatives of a scalar field, which we have identified in a previous work. These theories, whose degeneracy in general ensures the absence of Ostrogradski instability, include the quartic Horndenski Lagrangian as well as its quartic extension beyond Horndeski, but also other families of Lagrangians. We study how all these theories transform under general conformal-disformal transformations and find that they can be separated into three main classes that are stable under these transformations. This leads to a complete classification modulo conformal-disformal transformations. Finally, we show that these higher order theories include mimetic gravity and some particular khronometric theories. They also contain theories that do not correspond, to our knowledge, to already studied theories, even up to field redefinitions.

gr-qc↗

arXiv2015

Hamiltonian analysis of higher derivative scalar-tensor theories

We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of the dangerous Ostrogradski ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.

gr-qc↗

arXiv2015

Black hole spectroscopy from Loop Quantum Gravity models

Using Monte Carlo simulations, we compute the integrated emission spectra of black holes in the framework of Loop Quantum Gravity (LQG). The black hole emission rates are governed by the entropy whose value, in recent holographic loop quantum gravity models, was shown to agree at leading order with the Bekenstein-Hawking entropy. Quantum corrections depend on the Barbero-Immirzi parameter $γ$. Starting with black holes of initial horizon area $A \sim 10^2$ in Planck units, we present the spectra for different values of $γ$. Each spectrum clearly decomposes in two distinct parts: a continuous background which corresponds to the semi-classical stages of the evaporation and a series of discrete peaks which constitutes a signature of the deep quantum structure of the black hole. We show that $γ$ has an effect on both parts that we analyze in details. Finally, we estimate the number of black holes and the instrumental resolution required to experimentally distinguish between the considered models.

gr-qc↗

arXiv2015

Analytic continuation of real Loop Quantum Gravity : Lessons from black hole thermodynamics

This contribution is devoted to summarize the recent results obtained in the construction of an "analytic continuation" of Loop Quantum Gravity (LQG). By this, we mean that we construct analytic continuation of physical quantities in LQG from real values of the Barbero-Immirzi parameter $γ$ to the purely imaginary value $γ= \pm i$. This should allow us to define a quantization of gravity with self-dual Ashtekar variables. We first realized in [1] that this procedure, when applied to compute the entropy of a spherical black hole in LQG for $γ=\pm i$, allows to reproduce exactly the Bekenstein-Hawking area law at the semi-classical limit. The rigorous construction of the analytic continuation of spherical black hole entropy has been done in [2]. Here, we start with a review of the main steps of this construction: we recall that our prescription turns out to be unique (under natural assumptions) and leads to the right semi-classical limit with its logarithmic quantum corrections. Furthermore, the discrete and $γ$-dependent area spectrum of the black hole horizon becomes continuous and obviously $γ$-independent. Then, we review how this analytic continuation could be interpreted in terms of an analytic continuation from the compact gauge group $SU(2)$ to the non-compact gauge group $SU(1,1)$ relying on an analysis of three dimensional quantum gravity.

gr-qc↗

arXiv2014

Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy

We study the thermodynamical properties of black holes when described as gases of indistinguishable punctures with a chemical potential. In this picture, which arises from loop quantum gravity, the black hole microstates are defined by finite families of half-integers spins coloring the punctures, and the near-horizon energy measured by quasi-local stationary observers defines the various thermodynamical ensembles. The punctures carry excitations of quantum geometry in the form of quanta of area, and the total horizon area $a_\text{H}$ is given by the sum of these microscopic contributions. We assume here that the system satisfies the Bose-Einstein statistics, and that each microstate is degenerate with a holographic degeneracy given by $\exp\big(λa_\text{H}/\ell_\text{Pl}^2\big)$ and $λ>0$. We analyze in detail the thermodynamical properties resulting from these inputs, and in particular compute the grand canonical entropy. We explain why the requirements that the temperature be fixed to the Unruh temperature and that the chemical potential vanishes do not specify completely the semi-classical regime of large horizon area, and classify in turn what the various regimes can be. When the degeneracy saturates the holographic bound ($λ=1/4$), there exists a semi-classical regime in which the subleading corrections to the entropy are logarithmic. Furthermore, this regime corresponds to a Bose-Einstein condensation, in the sense that it is dominated by punctures carrying the minimal (or ground state) spin value $1/2$.

gr-qc↗

arXiv2014

Loop Quantum Cosmology with Complex Ashtekar Variables

We construct and study Loop Quantum Cosmology (LQC) when the Barbero-Immirzi parameter takes the complex value $γ=\pm i$. We refer to this new quantum cosmology as complex Loop Quantum Cosmology. We proceed in making an analytic continuation of the Hamiltonian constraint (with no inverse volume corrections) from real $γ$ to $γ=\pm i$ in the simple case of a flat FLRW Universe coupled to a massless scalar field with no cosmological constant. For that purpose, we first compute the non-local curvature operator (defined by the trace of the holonomy of the connection around a fundamental plaquette) evaluated in any spin $j$ representation and we find a new close formula for it. This allows to define explicitly a one parameter family of regularizations of the Hamiltonian constraint in LQC, parametrized by the spin $j$. It is immediate to see that any spin $j$ regularization leads to a bounce scenario. Then, motivated particularly by previous results on black hole thermodynamics, we perform the analytic continuation of the Hamiltonian constraint defined by $γ=\pm i$ and $j=-1/2+is$ where $s$ is real. Even if the area spectrum is now continuous, we show that the so-defined complex LQC removes also the original singularity which is replaced by a quantum bounce. In addition, the maximal density and the minimal volume of the Universe are obviously independent of $γ$. Furthermore, the dynamics before and after the bounce are no more symmetric, which makes a clear distinction between these two phases of the evolution of the Universe.

gr-qc↗

arXiv2014

Translation invariant time-dependent massive gravity: Hamiltonian analysis

The canonical structure of the massive gravity in the first order moving frame formalism is studied. We work in the simplified context of translation invariant fields, with mass terms given by general non-derivative interactions, invariant under the diagonal Lorentz group, depending on the moving frame as well as a fixed reference frame. We prove that the only mass terms which give 5 propagating degrees of freedom are the dRGT mass terms, namely those which are linear in the lapse. We also complete the Hamiltonian analysis with the dynamical evolution of the system.

hep-th↗

arXiv2014

Analytic Continuation of Black Hole Entropy in Loop Quantum Gravity

We define the analytic continuation of the number of black hole microstates in Loop Quantum Gravity to complex values of the Barbero-Immirzi parameter $γ$. This construction deeply relies on the link between black holes and Chern-Simons theory. Technically, the key point consists in writing the number of microstates as an integral in the complex plane of a holomorphic function, and to make use of complex analysis techniques to perform the analytic continuation. Then, we study the thermodynamical properties of the corresponding system (the black hole is viewed as a gas of indistinguishable punctures) in the framework of the grand canonical ensemble where the energy is defined á la Frodden-Gosh-Perez from the point of view of an observer located close to the horizon. The semi-classical limit occurs at the Unruh temperature $T_U$ associated to this local observer. When $γ=\pm i$, the entropy reproduces at the semi-classical limit the area law with quantum corrections. Furthermore, the quantum corrections are logarithmic provided that the chemical potential is fixed to the simple value $μ=2T_U$.

gr-qc↗

arXiv2014

Near-Horizon Radiation and Self-Dual Loop Quantum Gravity

We compute the near-horizon radiation of quantum black holes in the context of self-dual loop quantum gravity. For this, we first use the unitary spinor basis of $\text{SL}(2,\mathbb{C})$ to decompose states of Lorentzian spin foam models into their self-dual and anti self-dual parts, and show that the reduced density matrix obtained by tracing over one chiral component describes a thermal state at Unruh temperature. Then, we show that the analytically-continued dimension of the $\text{SU}(2)$ Chern-Simons Hilbert space, which reproduces the Bekenstein-Hawking entropy in the large spin limit in agreement with the large spin effective action, takes the form of a partition function for states thermalized at Unruh temperature, with discrete energy levels given by the near-horizon energy of Frodden-Gosh-Perez, and with a degenerate ground state which is holographic and responsible for the entropy.

gr-qc↗

arXiv2013

Black Hole Entropy from complex Ashtekar variables

In loop quantum gravity, the number $N_Γ(A,γ)$ of microstates of a black hole for a given discrete geometry $Γ$ depends on the so-called Barbero-Immirzi parameter $γ$. Using a suitable analytic continuation of $γ$ to complex values, we show that the number $N_Γ(A,\pm i)$ of microstates behaves as $\exp(A/(4\ell_\text{Pl}^2))$ for large area $A$ in the large spin semiclassical limit. Such a correspondence with the semiclassical Bekenstein-Hawking entropy law points towards an unanticipated and remarkable feature of the original complex Ashtekar variables for quantum gravity.

gr-qc↗

arXiv2013

BTZ Black Hole Entropy and the Turaev-Viro model

We show the explicit agreement between the derivation of the Bekenstein-Hawking entropy of a Euclidean BTZ black hole from the point of view of spin foam models and canonical quantization. This is done by considering a graph observable (corresponding to the black hole horizon) in the Turaev-Viro state sum model, and then analytically continuing the resulting partition function to negative values of the cosmological constant.

gr-qc↗

arXiv2013

Statistics, holography, and black hole entropy in loop quantum gravity

In loop quantum gravity the quantum states of a black hole horizon are produced by point-like discrete quantum geometry excitations (or {\em punctures}) labelled by spin $j$. The excitations possibly carry other internal degrees of freedom also, and the associated quantum states are eigenstates of the area $A$ operator. On the other hand, the appropriately scaled area operator $A/(8π\ell)$ is also the physical Hamiltonian associated with the quasilocal stationary observers located at a small distance $\ell$ from the horizon. Thus, the local energy is entirely accounted for by the geometric operator $A$. We assume that: In a suitable vacuum state with regular energy momentum tensor at and close to the horizon the local temperature measured by stationary observers is the Unruh temperature and the degeneracy of `matter' states is exponential with the area $\exp{(λA/\ell_p^2)}$---this is supported by the well established results of QFT in curved spacetimes, which do not determine $λ$ but asserts an exponential behaviour. The geometric excitations of the horizon (punctures) are indistinguishable. In the semiclassical limit the area of the black hole horizon is large in Planck units. It follows that: Up to quantum corrections, matter degrees of freedom saturate the holographic bound, {\em viz.} $λ=\frac{1}{4}$. Up to quantum corrections, the statistical black hole entropy coincides with Bekenstein-Hawking entropy $S={A}/({4\ell_p^2})$. The number of horizon punctures goes like $N\propto \sqrt{A/\ell_p^2}$, i.e the number of punctures $N$ remains large in the semiclassical limit. Fluctuations of the horizon area are small while fluctuations of the area of an individual puncture are large. A precise notion of local conformal invariance of the thermal state is recovered in the $A\to\infty$ limit where the near horizon geometry becomes Rindler.

gr-qc↗

arXiv2013

A note on the Holst action, the time gauge, and the Barbero-Immirzi parameter

In this note, we review the canonical analysis of the Holst action in the time gauge, with a special emphasis on the Hamiltonian equations of motion and the fixation of the Lagrange multipliers. This enables us to identify at the Hamiltonian level the various components of the covariant torsion tensor, which have to be vanishing in order for the classical theory not to depend upon the Barbero-Immirzi parameter. We also introduce a formulation of three-dimensional gravity with an explicit phase space dependency on the Barbero-Immirzi parameter as a potential way to investigate its fate and relevance in the quantum theory.

gr-qc↗

arXiv2013

Spectra of geometric operators in three-dimensional LQG: From discrete to continuous

We study and compare the spectra of geometric operators (length and area) in the quantum kinematics of two formulations of three-dimensional Lorentzian loop quantum gravity. In the SU(2) Ashtekar-Barbero framework, the spectra are discrete and depend on the Barbero-Immirzi parameter $γ$ exactly like in the four-dimensional case. However, we show that when working with the self-dual variables and imposing the reality conditions the spectra become continuous and $γ$-independent.

gr-qc↗