Searcharxiv⌕ Search

arXiv subjects

Alejandro Perez

Publications and source records attributed to Alejandro Perez.

At least 55 records · Page 3Linked to original sources
arXiv2015

No firewalls in quantum gravity: the role of discreteness of quantum geometry in resolving the information loss paradox

In an approach to quantum gravity where space-time arises from coarse graining of fundamentally discrete structures, black hole formation and subsequent evaporation can be described by a unitary evolution without the problems encountered by the standard remnant scenario or the schemes where information is assumed to come out with the radiation while evaporation (firewalls and complementarity). The final state is purified by correlations with the fundamental pre-geometric structures (in the sense of Wheeler) which are available in such approaches, and, like defects in the underlying space-time weave, can carry zero energy.

gr-qc↗
arXiv2015

Quantum Geometry and Black Holes

We present an overall picture of the advances in the description of black hole physics from the perspective of loop quantum gravity. After an introduction that discusses the main conceptual issues we present some details about the classical and quantum geometry of isolated horizons and their quantum geometry and then use this scheme to give a natural definition of the entropy of black holes. The entropy computations can be neatly expressed in the form of combinatorial problems solvable with the help of methods based on number theory and the use of generating functions. The recovery of the Bekenstein-Hawking law and corrections to it is explained in some detail. After this, due attention is paid to the discussion of semiclassical issues. An important point in this respect is the proper interpretation of the horizon area as the energy that should appear in the statistical-mechanical treatment of the black hole model presented here. The chapter ends with a comparison between the microscopic and semiclassical approaches to the computation of the entropy and discusses a number of issues regarding the relation between entanglement and statistical entropy and the possibility of comparing the subdominant (logarithmic) corrections to the entropy obtained with the help of the Euclidean path integral with the ones obtained in the present framework.

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

Statistical and entanglement entropy for black holes in quantum geometry

We analyze the relationship between entanglement (or geometric) entropy with statistical mechanical entropy of horizon degrees of freedom when described in the framework of isolated horizons in loop quantum gravity. We show that, once the relevant degrees of freedom are identified, the two notions coincide. The key ingredient linking the two notions is the structure of quantum geometry at Planck scale implied by loop quantum gravity, where correlations between the inside and outside of the black hole are mediated by eigenstates of the horizon area operator.

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

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

Statistical Entropy of a BTZ Black Hole from Loop Quantum Gravity

We compute the statistical entropy of a BTZ black hole in the context of three-dimensional Euclidean loop quantum gravity with a cosmological constant $Λ$. As in the four-dimensional case, a quantum state of the black hole is characterized by a spin network state. Now however, the underlying colored graph $Γ$ lives in a two-dimensional spacelike surface $Σ$, and some of its links cross the black hole horizon, which is viewed as a circular boundary of $Σ$. Each link $\ell$ crossing the horizon is colored by a spin $j_\ell$ (at the kinematical level), and the length $L$ of the horizon is given by the sum $L=\sum_\ell L_\ell$ of the fundamental length contributions $L_\ell$ carried by the spins $j_\ell$ of the links $\ell$. We propose an estimation for the number $N^\text{BTZ}_Γ(L,Λ)$ of the Euclidean BTZ black hole microstates (defined on a fixed graph $Γ$) based on an analytic continuation from the case $Λ>0$ to the case $Λ<0$. In our model, we show that $N^\text{BTZ}_Γ(L,Λ)$ reproduces the Bekenstein-Hawking entropy in the classical limit. This asymptotic behavior is independent of the choice of the graph $Γ$ provided that the condition $L=\sum_\ell L_\ell$ is satisfied, as it should be in three-dimensional quantum gravity.

gr-qc↗
arXiv2012

Modelling black holes with angular momentum in loop quantum gravity

We construct a SU(2) connection formulation of Kerr isolated horizons. As in the non-rotating case, the model is based on a SU(2) Chern-Simons theory describing the degrees of freedom on the horizon. The presence of a non-vanishing angular momentum modifies the admissibility conditions for spin network states. Physical states of the system are in correspondence with open intertwiners with total spin matching the angular momentum of the spacetime.

gr-qc↗
arXiv2012

The scaling of black hole entropy in loop quantum gravity

We discuss some general properties of black hole entropy in loop quantum gravity from the perspective of local stationary observers at distance l from the horizon. The present status of the theory indicates that black hole entropy differs from the low energy (IR) expected value A/(4G) (in natural units) in the deep Planckian regime (UV). The partition function is well defined if the number of non-geometric degrees of freedom g_M (encoding the degeneracy of the area a_p eigenvalue at a puncture p) satisfy the holographic bound g_M < exp(ap/(4G)). Our framework provides a natural renormalization mechanism such that S_UV ---> S_IR=A/(4 G) as the scale l flows.

gr-qc↗
arXiv2012

The Spin Foam Approach to Quantum Gravity

This article reviews the present status of the spin foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently introduced new models for four dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self-contained treatment of the 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.

gr-qc↗
arXiv2012

The new spin foam models and quantum gravity

In this article we give a systematic definition of the recently introduced spin foam models for four dimensional quantum gravity reviewing the main results on their semiclassical limit on fixed discretizations.

gr-qc↗
arXiv2011

Black hole entropy and isolated horizons thermodynamics

We present a statistical mechanical calculation of the thermodynamical properties of (non rotating) isolated horizons. The introduction of Planck scale allows for the definition of an universal horizon temperature (independent of the mass of the black hole) and a well-defined notion of energy (as measured by suitable local observers) proportional to the horizon area in Planck units. The microcanonical and canonical ensembles associated with the system are introduced. Black hole entropy and other thermodynamical quantities can be consistently computed in both ensembles and results are in agreement with Hawking's semiclassical analysis for all values of the Immirzi parameter.

gr-qc↗
arXiv2011

A local first law for black hole thermodynamics

We first show that stationary black holes satisfy an extremely simple local form of the first law δE=κ(l) δA/(8 π) where the thermodynamical energy E=A/(8πl) and (local) surface gravity κ(l)=1/l, where A is the horizon area and l is a proper length characterizing the distance to the horizon of a preferred family of local observers suitable for thermodynamical considerations. Our construction is extended to the more general framework of isolated horizons. The local surface gravity is universal. This has important implications for semiclassical considerations of black hole physics as well as for the fundamental quantum description arising in the context of loop quantum gravity.

gr-qc↗
arXiv2011

Non-commutative holonomies in 2+1 LQG and Kauffman's brackets

We investigate the canonical quantization of 2+1 gravity with Λ > 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 \surdΛe, 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_λ = A + λe 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.

gr-qc↗
arXiv2011

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 $Λ>0$ 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 $A$ and the canonically conjugate triad field $e$. A natural regularization of the constraints of 2+1 gravity can be defined in terms of the holonomies of $A+=A + \sqrtΛe$. As a first step towards the quantization of these constraints we study the canonical quantization of the holonomy of the connection $A_λ=A+λe$ 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.

gr-qc↗
arXiv2011

Static isolated horizons: SU(2) invariant phase space, quantization, and black hole entropy

We study the classical field theoretical formulation of static generic isolated horizons in a manifestly SU(2) invariant formulation. We show that the usual classical description requires revision in the non-static case due to the breaking of diffeomorphism invariance at the horizon leading to the non conservation of the usual pre-symplectic structure. We argue how this difficulty could be avoided by a simple enlargement of the field content at the horizon that restores diffeomorphism invariance. Restricting our attention to static isolated horizons we study the effective theories describing the boundary degrees of freedom. A quantization of the horizon degrees of freedom is proposed. By defining a statistical mechanical ensemble where only the area A of the horizon is fixed macroscopically-states with fluctuations away from spherical symmetry are allowed-we show that it is possible to obtain agreement with the Hawking's area law---S = A/4 (in Planck Units)---without fixing the Immirzi parameter to any particular value: consistency with the area law only imposes a relationship between the Immirzi parameter and the level of the Chern-Simons theory involved in the effective description of the horizon degrees of freedom.

gr-qc↗