The purpose of this talk is to give an overview of the development and the various branches of the Hamiltonian approach to quantum gravity, with focus on its dynamics, over the past decades.
The quantum state of the flat Ashtekar-Barbero connection is quite well defined in Loop Quantum Gravity theory as an element of the dual space to cylindrical functions. This state is not pathological at all, as Jorge Pullin noticed many years ago, and it can be treated as vacuum. From Pullin's vacuum, other states can be generated using LQG operators. It is easy to construct from them partial...
I will discuss the Lorentzian quantum gravity path integral in simplicial approaches like Regge calculus and spin foams. I will draw connections between three different aspects of the Lorentzian path integral: firstly the appearance of light cone irregular configurations, which result in a surprising ambiguity for the Lorentzian path integral, secondly the fate of spike configurations in the...
The conceptual and computational progresses in the covariant framework of LQG have brought a number of results in its application to cosmology. In this talk I highlight some of the most interesting steps forward in spinfoam cosmology. I briefly review the general assumption in defining the cosmological model. I focus then on the development of a novel strategy to compute cosmological...
The problem of obtaining and interpreting solutions to the quantum Hamilton constraint of LQG is a long-standing and difficult one. We approach this problem with novel numerical methods which leverage the power of neural networks, therefore taking the first step in applying deep learning methods in LQG.
We present the basic idea of parameterizing quantum states with a neural network, and...
Despite common assumptions that canonical and covariant hamiltonian methods yield equivalent physical theories, we revisit the issue and show that, after properly identifying what one might mean by equivalence, there are instances in which these two methods are indeed inequivalent when boundaries are present.
Based on the exact holographic duality formula related the Ponzano-Regge amplitudes for 3d quantum gravity and the 2d inhomogeneous Ising model, I will clarify the relation between bulk path integrals and boundary theory in the context of spinfoams. Through simple toy-models, I will explain how bulk observables become the coupling constants of the boundary theory, and vice-versa how the bulk...
The asymptotic safety (ASQG) and canonical (CQG) approach to quantum gravity have been developed to a large extent independent of each other. In this work we take first steps to bringing them into closer contact by working with the Lorentzian version of the functional renormalisation group of ASQG which we relate to the reduced phase space formulation of CQG.
Quantum gravitational tunneling effects are expected to give rise to a number of interesting observable phenomena, including, in particular, the evolution of black holes at the end of their existence. Covariant Loop Quantum Gravity provides a framework to study these phenomena, yet a precise identification of tunneling processes is still not known. Motivated by tunneling processes, I will...
We explore the modifications to the fundamental geometric variables due to the inclusion of fermions and the resulting gravitational dynamics. Finally we speculate on how to proceed with the quantization of the system.
Computing spin foam amplitudes explicitly is still a challenging task, in particular for 2-complexes consisting of multiple vertices. In this talk I will present three algorithms that will help construct and compute amplitudes more efficiently.
The first algorithm allows us to easily construct 2-complexes and the associated amplitude. We define the number of spin foam vertices and choose...
Are the atoms of space distinguishable? In this talk I discuss recent developments on the construction of a diffeomorphism invariant notion of entanglement entropy of a region in loop quantum gravity and spinfoams.
The investigation of boundary charges in asymptotically flat spacetime draw a lot of attention recent years, which has provided us valuable insight and significantly enhanced our general understanding of gravity. However, most of previous studies along this line are based on the traditional general relativity, which is a pure constraint theory in the bulk. The boundary charges based on the...
In this talk I will present a framework which allows to construct effective LTB models starting from a polymerized spherical symmetric model. Then I will focus on dust collapses and show how these results can be related via coordinate transformations to other models in the literature. At last I want to analyze polymerized vacua and explore the formulation of a Birkhoff like theorem as well as...
How complex is the structure of quantum geometry? In loop quantum gravity, atoms of space are SU(2) 4-valent intertwiners, which describe quantum tetrahedra. The complexity of this construction has a concrete consequence in recent efforts to simulate quantum geometry models and toward experimental demonstrations of quantum gravity effects. There is, then, a computational and an experimental...
To study the large-j asymptotics of Lorentzian spinfoam EPRL models on complex four dimensional geometries with internal points, it is crucial to first understand the underlying impact of geometrical structures on the spinfoam amplitudes, due to the existence of continuous critical points and their non-trivial contribution in the covariant path integral formalism. In this paper we propose...
Spin foams arose as the covariant (path integral) formulation of quantum gravity depicting transition amplitudes between different quantum geometry states. Though a lot of progress has been made in defining the underlying mathematics, actually calculating the corresponding amplitudes is still a challenging topic, especially for more complicated, thus more physically-relevant cases. Following...
Black hole perturbations are mostly considered up to second order. In this talk we investigate the problem of incorporating perturbations of higher than second order and the new technical challenges that arise.
We explore spherically symmetric black-hole models with corrections motivated by loop quantum gravity. We derive a general family of Hamiltonians satisfying specific covariance conditions so that the dynamics generated by such families define a spacetime geometry independently of gauge or coordinate choices. By construction, there are no propagating degrees of freedom, but we show that the...
The Barbero-Immirzi parameter appears in the EPRL spinfoam model via a duality rotation. In an effective field theory description, this duality rotation results in a relation between the coupling constants of parity-even and parity-odd higher-curvature terms. We study cosmic inflation in this effective theory and show that the observation of a primordial tensor polarization, together with the...
In this talk, we develop a quantum theory of homogeneously curved tetrahedron geometry, by applying the combinatorial quantization to the phase space of tetrahedron shapes defined in arXiv:1506.03053. Our method is based on the relation between this phase space and the moduli space of SU(2) flat connections on a 4-punctured sphere. The quantization results in the physical Hilbert space as the...
Abstract: This work examines a family of loop quantizations for the classical Kruskal spacetimes using the effective description motivated from loop quantum gravity for four generic parameters, $c_o, m, \delta_b$, and $\delta_c$, where the latter two denote the polymerization parameters capturing the underlying quantum geometry. The focus lies on the family where polymerization parameters...
This talk reports on a recent proposal for a Lorentzian spin-foam coherent amplitude in 2+1 dimensions, defined for an arbitrary combination of space- and time-like edges. The construction makes use of a new set of boundary coherent states, derived from the correspondence between Majorana spinors and space-like 2+1 vectors. The amplitude is shown to recover the Lorentzian Regge action in the...
Considerable attention has been paid to the study of the quantum geometry of nonrotating black holes within the framework of Loop Quantum Cosmology. This interest has been reinvigorated since the introduction of a novel effective model by Ashtekar, Olmedo, and Singh. Despite recent advances in its foundation, there are certain questions about its quantization that still remain open. Here we...
Area metrics generalize spacetime geometry based on lengths and provide a candidate parametrization of the extended configuration space of loop quantum gravity and spin foams in the semiclassical regime. On this basis, I will consider generally covariant actions to second order in area metric fluctuations and derivatives. The effective actions for the subset of area metric degrees of freedom...
We use emergent modified gravity as a covariant, effective framework for obtaining black hole solutions in loop quantum gravity with an arbitrary, scale-dependent holonomy parameter λ in vacuum spherical symmetry. The construction is robust and can be applied in general for any type of triangulation. We obtained vacuum solutions not only for asymptotically flat spacetime but also for dS and...
Can one compute thermodynamic quantities, such as entropy, with a Lorentzian path integral? Using a regularization of the path integral via Regge calculus, we will see that the answer is affirmative.
Irregularities in the light cone structure, e.g. configurations with contractible closed timelike curves, play an essential role for this conclusion. Such light cone irregularities contribute...
Following the techniques of canonical loop quantum gravity, a full Thiemann regularization is performed on the scalar constraint of classical general relativity. The regularized Hamiltonian is then considered for a general spherically-symmetric spacetime, without recourse to additional gauge-fixing conditions commonly imposed to aid in computing the radial holonomies. By investigating the form...
We expect quantum field theories for matter to acquire intricate corrections due to their coupling to quantum fluctuations of the gravitational field. This can be precisely worked out in 3D quantum gravity: after integrating out quantum gravity, matter fields are effectively described as non-commutative quantum field theories, with quantum-deformed Lorentz symmetries. An open question...
While there are many fascinating results on quantum black holes and their evaporation in LQG, the focus tends to be on singularity resolution and the structure of the
quantum-extended space-time. Issues of entanglement and recovery of information, that
originally sparked interest in black hole evaporation in the wider physics community, have
not received the attention they deserve. The goal...
By using the regularization freedom of the Hamiltonian constraint for loop quantum gravity, the observational cosmological constant can emerge at large volume limit from the model of loop quantum cosmology, and the effective Newtonian constant satisfies the experimental restrictions in the meantime. Therefore, the so-called dark energy could be an emergent effect of LQG.
Primordial black holes have grown in popularity as a dark matter candidate. Different mass spectrum for them are currently under consideration. In this talk I discuss how Loop Quantum Cosmology can integrate the presence of primordial black holes, either in an inflationary scenario or in a ekpyrotic scenario. I review some recent results and discuss the current work in progress. I focus in...
We show how cosmological dynamics can be mapped to hydrodynamics (on minisuperspace) via field symmetries. We then connect the same hydrodynamics (on minisuperspace) to several quantum gravity directions, starting from group field theory, and argue that it may represent a general effective framework for the cosmological sector of quantum gravity.
We consider 4d spherical collapse of a massless scalar field with a novel Areal Radius dependent coupling and obtain the following results:
(i) classical collapse is described by the Vaidya solution (ii) quantum back reaction can be explicitly computed (iii) the semiclassical solution
describes black hole formation, subsequent evaporation along a timelike `dynamical horizon' and a back...
We present a description of axial perturbations in Kantowski-Sachs spacetimes, corresponding to nonrotating, uncharged black hole interiors. Perturbations are expressed in terms of perturbative gauge invariants, linear perturbative constraints, and their momenta. Moreover, the entire system formed by these perturbations and the background degrees of freedom is described by a canonical set of...
We analyze the evolution of scalar cosmological perturbations in a closed universe on a background described by a loop quantum cosmology model with an inflationary regime consistent with the constraints on inflation set by the observations of the CMB by the Planck mission. Initial conditions for the perturbations are set before the bounce, and the perturbations are numerically evolved until...
We study analytical approximate solutions for second-order homogeneous differential equations with the existence of only two turning points (but without poles) by using the uniform asymptotic approximation (UAA) method. To be more concrete, we consider the Pöschl-Teller (PT) potential, for which analytical solutions are known. Depending on the values of the parameters involved in the PT...
Author: Álvaro Torres-Caballeros Instituto de Estructura de la Materia, IEM-CSIC Serrano 121, 28006 Madrid, Spain alvaro.torres@iem.cfmac.csic.es Co-authors: Jerónimo Cortez Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México. Ciudad de México 04510, Mexico jacq@ciencias.unam.mx Beatriz Elizaga Navascués Department of Physics and Astronomy, Louisiana State...
The Oppenheimer-Snyder model is the prototypical example of black hole formation by gravitational collapse. It predicts that a black hole horizon is formed once a star collapses to within its own Schwarzschild radius. After that, the collapsing matter reaches Planckian densities in a short proper time. What happens next is outside the reach of general relativity, as it involves the quantum...
The evolution of the universe in modified loop quantum cosmologies exhibits universal properties for sharply peaked states, similar to that in the standard loop quantum cosmology (LQC). In this talk, I shall present our recent investigations on such universal properties for the modified loop quantum cosmological model I (mLQC-I), by paying particular attention to the evolution before the...
In Loop Quantum Cosmology (LQC), as in any other quantum theory, various regularizations of the Hamiltonian constraint and quantum ambiguities yield distinct physical implications. Specifically, the treatments of the Euclidean and Lorentzian parts of the Hamiltonian constraint for spatially flat, homogeneous, and isotropic spacetime before quantization results in alternative quantizations of...
The black hole information puzzle can be solved if two conditions are met: information about what falls inside a black hole must remain encoded in d.o.f that persist after the black hole has completely evaporated. Moreover, these d.o.f must not contribute significantly to the energy of the system, given that the macroscopic mass of the initial black hole has been radiated to infinity in the...
Homogenous cosmological models and black holes belong to classes of space-time metrics defined in terms of a finite number of degrees of freedom. For these, the dynamics reduces to a one-dimensional mechanical model. It is then easy to investigate their classical symmetries and the corresponding Noether charges.
These dynamical symmetries have a geometric interpretation, not in terms of...
Understanding the fundamental factors which shape the quantum structure of spacetime in loop quantized Bianchi-IX spacetimes offers valuable insights into the generic resolution of singularities and discerning the significance of anisotropies in the Planck regime. Conversely, it has been argued that ekpyrosis could mitigate the effects of anisotropies. Further, recent investigations into the...
Covariant LQG predicts that the end of the black hole evaporation leaves a long-living remnant described by a white hole geometry, and stabilized by the LQG area gap. This result provides an intriguing candidate for dark matter, which does not require any new physics besides General Relativity and quantum theory,
We present the classical-quantum (CQ) hybrid dynamics of homogeneous cosmology from a Hamiltonian perspective where the classical gravitational phase space variables and matter state evolve self-consistently with full backreaction. We compare numerically the classical and CQ dynamics for isotropic and anisotropic models, including quantum scalar-field induced corrections to the Kasner...
Effective models of gravitational collapse in loop quantum gravity for the Lemaître-Tolman-Bondi spacetime predict that collapsing matter reaches a maximum finite density, bounces, and then expands outwards. I explain how in the marginally bound case, shell-crossing singularities commonly occur for inhomogeneous initial profiles of the dust energy density; this is the case in particular for...
I will present an ongoing work about the evolution of a two-field bouncing scenario in Loop Quantum Cosmology. The model features a quasi-dust field with a slightly negative equation of state, dominating in the far past of the contraction phase, which is known as a possible candidate to explain the red tilt observed in the CMB power spectrum. To avoid instabilities, an ekpyrotic field...
The collapse of a spherically symmetric ball of dust has been intensively studied in Loop Quantum Gravity (LQG). From a quantum theory, it is possible to recover a semiclassical regime through a polymerization procedure. In this setting, general solutions to the Polymerized Einstein Field Equations (PEFE) will be discussed both for the interior and the exterior of the dust cloud. Exterior...
At the end of its evaporation, a black hole may leave a remnant where a large amount of information is stored. We argue that the existence of an area gap as predicted by Loop Quantum Gravity removes a main objection to this scenario. Remnants should radiate in the low-frequency spectrum. We model this emission and derive properties of the diffuse radiation emitted by a population of such...
We provide a new picture for the emergence of a bouncing cosmology at a pure quantum level, according to the idea that a semiclassical behavior of the Universe towards the singularity is not available in many relevant Minisuperspace models. In particular, we clarify how any Bianchi I localized wave packet unavoidably spreads when the singularity is approached, and therefore the semiclassical...
A notion of residual diffeomorphism covariance in quantum Kantowski-Sachs (KS), describing the interior of a Schwarzschild black hole will be introduced, and the solution for the family of Hamiltonian constraint operators satisfying the condition will be briefly presented.
The result will then be compared to Hamiltonian constraints proposed for Loop Quantum KS in the literature, especially...
Next generation CMB experiments may provide stronger constraints for primordial observables that are sensitive to the semi-classical regime of quantum gravity. Here we present some tools to compare the predictions for the primordial power spectrum, tilt, running and running-of-the-running given by generic models of slow-roll inflation. These tools have been used in an effective field theory...
I will discuss a class of time-dependent, asymptotically flat and spherically symmetric metrics which model gravitational collapse in quantum gravity developed by myself and the other listed authors. Motivating the work was the intuition that quantum gravity should not exhibit curvature singularities and indeed, the metrics lead to singularity resolution with horizon formation and evaporation...
We address the problem of the SU(2) internal symmetry in Loop Quantum Cosmology (LQC) and its relationship with canonical Loop Quantum Gravity (LQG). We introduce new tools to treat non-diagonal Bianchi models in LQC, and we discuss the Gauss constraint and the role of gauge freedom. This allows us to prove that, in the minisuperspace cosmological framework, there exist suitable variables in...
We construct the full spacetime of a minimal uncertainty inspired black hole, borrowing the improved prescription from loop quantum gravity. In the minimal uncertainty approach, minimalization of the uncertainty relations leads to the deformation of the algebra leading to an effective theory. We show that the asymptotic and classical limits of our model match the Schwrazschild solution, and...
We explain the analysis of the compact binary system dynamics in the Post-Newtonian approach adding the cosmological constant $\Lambda$ at the first Post-Newtonian (PN) order from the Einstein-Hilbert action. Considering small values of $\Lambda$ we find that it plays the role of a PN factor, and we us this feature to compute the Lagrangian of a binary compact system at the center of mass...
The concept of spacetime discreteness is a common feature in quantum gravity theories. Recently, it has been speculated that the presence of discrete fundamental degrees of freedom should ultimately manifest, at least in the low-energy regime, in the form of diffusive effects, just as the presence of molecules generates diffusion in fluids. As for an effective description, such dissipation...
In asymptotically flat quantum gravity, the dimension of the Hilbert space is given by the exponential of the Bekenstein-Hawking entropy. Can we understand this thermodynamic entropy as a consequence of entanglement in a typical state at a definite ADM energy? We approach this question by exploring the behavior of the typical entanglement entropy in large quantum systems under constraints....
My talk will review how cosmological observations can be used to test quantum gravity, and also to provide some guidance for future progress. I will discuss how to make contact with cosmological data from loop quantum cosmology, observational constraints on the realization of various cosmological scenarios (such as inflation, ekpyrosis and the matter bounce) within loop quantum cosmology, as...
In this talk, I will overview the 4-dimensional Lorentzian spinfoam model with a non-vanishing cosmological constant and discuss its inviting properties, namely (1) that it gives finite spinfoam amplitude for any spinfoam graph, (2) that it is consistent with general relativity with a non-zero cosmological constant at its classical regime and (3) that there exists a feasible, concrete and...
One property that characterizes a black hole is that it maximizes entropy in a finite region with a fixed surface area. It may be a more fundamental one than the existence of a horizon in the context of quantum gravity, where there is no notion of continuum geometry. Using this characterization, we consider the interior of a black hole in the 4D semi-classical Einstein equation. For...
Open quantum systems provide a framework in which models for gravitationally induced decoherence can be formulated. In this talk a microscopic quantum mechanical model for gravitationally induced decoherence introduced by Blencowe and Xu is investigated in the context of neutrino oscillations. The focus lies on the
comparison with existing phenomenological models and the physical...
Entangled states in quantum field theory are not the exception but rather the norm. Even seemingly simple states such as the vacuum in Minkowski or Sitter spacetime are rich in the entanglement they contain. In this presentation, I will discuss recently developed techniques aimed at uncovering and characterizing the distribution of entanglement in field theory. These tools include the...
A major challenge at the interface between quantum gravity and cosmology is to understand how cosmological structures can emerge from physics at the Planck scale. In this talk, I will provide a concrete example of such an emergence process by extracting the physics of scalar and isotropic cosmological perturbations from full quantum gravity, as described by a causally complete Barrett-Crane...
When describing a physical system, it is very common to do so with respect to a reference frame - a ruler used to determine the position of a particle, for example, or a clock, which tracks the time that elapses while it is moving. Usually, reference frames are treated as purely classical objects with well-defined properties. But what happens if we take into account the quantum properties of...
In this talk, I discuss recent advances in Lorentzian quantum cosmology using group field theory (GFT) condensate cosmology and effective spin foams.
First, in the GFT approach, I introduce the complete Barrett-Crane (cBC) TGFT model coupled to four scalar fields, establishing a connection between the causal character of quantum geometry and relational scalar clock and rods. This allows to...
We derive a “classical-quantum” approximation scheme for a broad class of bipartite quantum systems from fully quantum dynamics. In this approximation, one subsystem evolves via classical equations of motion with quantum corrections, and the other subsystem evolves quantum mechanically with equations of motion informed by the evolving classical degrees of freedom. Using perturbation theory, we...
"3D gravity in tetrad variables shows a rich symmetry structure that includes both rotations and Kalb-Ramond translations which has been instrumental in understanding its properties. Therefore, extensions of this type of symmetries to the four-dimensional case, like the $\mathfrak{isu}(2)$-algebra described in [1910.05642] for Loop Quantum Gravity, may be crucial in understanding states of...
Time-dependent reflective boundary conditions (i.e. a moving mirror) in a scalar field theory in 1+1 dimensions have the power to model key aspects of Hawking radiation. In particular, this valuable pedagogical tool allows one to understand how early thermal quanta could be purified by late field modes. In this talk, we discuss a mirror trajectory that mimics an evaporating black hole; with a...
Abstract: Quantum gravitational theories generically suffer from issues such as the problems of normalizability, time and classical limit. Despite decades of technically sophisticated efforts, based on the orthodox quantum formulation, there remains a lack of consensus on these issues. In this talk, I will develop the viewpoint that these issues are not technical but conceptual, rooted in...
A covariant and conformally invariant approach to the symplectic structure of gravitational fields is natural to introduce when considering spacetimes with a nonzero cosmological constant. It utilizes the Normal Conformal Cartan Connection as a fundamental element of construction. The resulting symplectic potential is explicitly conformally invariant. One consequence is the regular behavior of...
In 3d gravity with a cosmological constant, it has been shown that discretizing homogeneously curved geometries requires Poisson Lie group structures. This naturally appears when gluing 2d curved building blocks. At the quantum level, this building blocks are labeled with intertwiners defined in terms of quantum group representations.
To generalize this construction to the 4D case with a...
One of the most basic notions in physics is the partitioning of a system into subsystems, and the study of correlations among its parts. Operationally, subsystems are distinguished by physically accessible observables which are often implicitly specified relative to some external frame, such as the laboratory, or a background notion of locality. In absence of external relata (as in...
The membrane paradigm illustrates a profound link between gravity on a stretched horizon and hydrodynamics. While this connection has been explored semi-classically, it holds potential for illuminating fundamental aspects of quantum spacetime, such as degrees of freedom, symmetries, and dynamics. In this work, we revisit the membrane viewpoint and introduce the concept of stretched Carroll...
The enhancement of the symmetry group for asymptotically flat spacetimes from the Poincare group to the infinite-dimensional BMS group gives a rich structure to the theory. The existence of supertranslations in the BMS group plays a key role in a variety of asymptotic phenomenon. In particular, there is a well-known "supertranslation ambiguity" in defining the angular momentum of an isolated...
We consider the quantization of gravity as an SL(2,C) gauge theory in terms of Ashtekar's selfdual variables and reality conditions for the spatial metric (RCI) and its evolution (RCII).
We start from a holomorphic phase space formulation and consider holomorphic cylindrical wave functions over SL(2,C) connections. We use an overall phase ambiguity of the complex selfdual action to obtain...
We will report on the latest advances within the program of generalized spinfoam models using the framework of higher gauge theory. This framework, based on the idea of describing gauge symmetry using 2-groups, 3-groups and other higher-order categorical structures, has the advantage of treating both matter and gravity on an equal footing, which allows us to discuss matter-related topics such...
In recent years there has been a renewed interest in the mathematical structure and gravitational physics of the null asymptote, in both classical and quantum regimes. From Carrollian Geometries, BMS symmetry, and the radiative phase space to quantization of null data, asymptotic graviton states, and infrared sectors, there is a vast ocean of mathematics and physics that can be learned from...
A 4-dimensional generally covariant gauge theory with local degrees of freedom is presented. It leads to the Gauss constraint but lacks both the Hamiltonian and spatial diffeomorphism constraints. The canonical theory therefore resembles Yang-Mills theory without the Hamiltonian. We describe its observables, quantization, and some generalizations.
Computations in canonical loop quantum gravity are severely hindered by the graph-changing nature of the scalar Hamiltonian constraint. In fact, not even the action of this constraint on 4-valent spin-network vertices has been fully derived in the literature to date. For this reason, drastic approximations, such as graph-non-changing constraints, are usually implemented. In order to overcome...
The Kerr spacetime hypothesis can be tested by using two approaches namely the top-bottom approach and bottom-up approach. The first one involves introducing the deviations in the Kerr metric through a theoretical model. The second approach involves introducing the deviations in terms of parameters. The metric proposed by Johannsen and Psaltis is one such parametrically deformed Kerr...
By assuming matter can oscillate in proper time, we demonstrate that a matter field with proper time oscillations can mimic the properties of a bosonic field. The particles observed are proper time oscillators. The assumption also gives rise to properties that can reduce differences between quantum theory and general relativity, e.g., self-adjoint internal time operator and proper time...
We present a Chern-Simons theory for the (2+1)-dimensional analog self-dual gravity theory that is based on the gauge group $SL(2,\mathbb{C})_ \mathbb{R}\triangleright\!\!\!< \mathbb{R}^6$. This is formulated by mapping the $3d$ complex self-dual dynamical variable and connection to $6d$ real variables which combines into a $12d$ Cartan connection.
Quantization is given by the...
Using properties of diffusion according to a quantum heat kernel constructed as an expectation over classical heat kernels on $S^1$, we probe the non-manifold-like nature of quantized space in a model of (1+1)-dimensional quantum gravity. By computing the mean squared displacement of a diffusing particle, we find that diffusion is anomalous, behaving similarly to that on a porous substrate,...
This presentation looks into the realm of black hole thermodynamics, emphasizing its connection with boundary conditions. We will explore how various boundary conditions impact the thermodynamic properties of black holes and examine the geometric interpretations of different thermodynamic potentials. By studying the first laws of thermodynamics, we aim to unravel the interesting connection...
We want to explore suitable boundary conditions for the asymptotically flat scenario of general relativity presented in terms of Ashtekar-Barbero variables. While the standard parity conditions have been already extensively studied, it turns out that they fail to produce non-trivial supertranslations at spatial infinity. We propose new parity conditions for the Ashtekar-Barbero variables that...
