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The aim of the present work is to demonstrate the applicability of machine learning techniques and in particular neural network quantum states in the context of loop quantum gravity, albeit for a simplified theory. We consider 3-dimensional Euclidean gravity in a gauge theoretical formulation in a certain weak coupling limit due to Smolin, and show that the gauge group becomes Abelian, resulting in U (1) 3 BF-theory. The theory is quantised using loop quantum gravity methods. The kinematical degrees of freedom are truncated, on account of computational feasibility, by fixing a graph and deforming the algebra of the holonomies to impose a cutoff on the charge vectors. This leads to a quantum theory related to U q (1) 3 BF-theory. The effect of imposing the cutoff on the charges is examined. We also implement the quantum volume operator of 3d loop quantum gravity. Most importantly we compare two constraints for the quantum model obtained: a master constraint enforcing curvature and Gauß constraint, as well as a combination of a quantum Hamilton constraint constructed using Thiemann's strategy and the Gauß master constraint. The two constraints are solved using the neural network quantum state ansatz, demonstrating its ability to explore models which are out of reach for exact numerical methods. The solutions spaces are quantitatively compared and although the forms of the constraints are radically different, the solutions turn out to have a surprisingly large overlap. We also investigate the behavior of the quantum volume in solutions to the constraints. [ABSTRACT FROM AUTHOR]

Many previous works have studied gravitational lensing effects from Loop Quantum Gravity. So far, gravitational lensing effects from Loop Quantum Gravity have only been studied by choosing large quantum parameters much larger than the Planck scale. However, by construction, the quantum parameters of the effective models of Loop Quantum Gravity are usually related to the Planck length and, thus, are extremely small. In this work, by strictly imposing the quantum parameters as initially constructed, we study the true quantum corrections of gravitational lensing effects by five effective black hole models of Loop Quantum Gravity. Our study reveals several interesting results, including the different scales of quantum corrections displayed by each model and the connection between the quantum correction of deflection angles and the quantum correction of the metric. Observables related to the gravitational lensing effect are also obtained for all models in the case of SgrA* and M87*. [ABSTRACT FROM AUTHOR]

Integrating loop quantum gravity with classical gravitational collapse models offers an effective solution to the black hole singularity problem and predicts the formation of a white hole in the later stages of collapse. Furthermore, the quantum extension of Kruskal spacetime indicates that white holes may convey information about earlier companion black holes. Photons emitted from the accretion disks of these companion black holes enter the black hole, traverse the highly quantum region, and then re-emerge from white holes in our universe. This process enables us to observe images of the companion black holes' accretion disks, providing insights into quantum gravity. In our study, we successfully obtained these accretion disk images. Our results indicate that these accretion disk images are confined within a circle with a radius equal to the critical impact parameter, while traditional accretion disk images are typically located outside this circle. As the observational angle increases, the accretion disk images transition from a ring shape to a shell-like shape. Furthermore, the positional and width characteristics of these accretion disk images are opposite to those of traditional accretion disk images. These findings provide valuable references for astronomical observations aimed at validating the investigated quantum gravity model. [ABSTRACT FROM AUTHOR]

From a dynamical systems point of view, a trivalent spin network model in Loop Quantum Gravity is considered, which presents self‐organized criticality (SOC), arising from a spin propagation dynamics. A partition function is obtained for the domains of stability connecting gauge non‐invariant avalanches, leading to an entropy formula for the asymptotic SOC state. The microscopic origin of this SOC entropy is therefore given by the excitation‐relaxation spin dynamics in the avalanche cycle. The puncturing of trivalent spin networks (TSN) edges participating in the avalanche are counted in terms of an ensemble perimeter over the implicit avalanches. By identifying this perimeter with that of an isolated (2+1)$(2+1)$‐D black hole horizon, it is conjectured that the SOC entropy reduces to the Bekenstein‐Hawking perimeter‐entropy law for the Bañados, Teitelboim, and Zanelli (BTZ) black hole, by an appropriate adjustment of a potential function based on the thermodynamical formalism of Sinai, Ruelle, and Bowen. [ABSTRACT FROM AUTHOR]

In this paper, we study the quantum geometric effects near the locations where classical black hole horizons used to appear in Einstein’s classical theory, within the framework of an improved dynamic approach, in which the internal region of a black hole is modeled by the Kantowski-Sachs (KS) spacetime and the two polymerization parameters are functions of the phase space variables. Our detailed analysis shows that the effects are so strong that black and white hole horizons of the effective quantum theory do not exist at all and instead are replaced by transition surfaces, across which the metric coefficients and their inverses are smooth and remain finite, as are the corresponding curvatures, including the Kretschmann scalar. These surfaces always separate trapped regions from anti-trapped regions. The number of such surfaces is infinite, so the corresponding KS spacetimes become geodesically complete, and no black and white hole-like structures exist in this scheme. [ABSTRACT FROM AUTHOR]

The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin foam models of quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin foam model and discuss the role of the causal structure in the reconstruction of a semiclassical space–time geometry. [ABSTRACT FROM AUTHOR]

In this paper, we explore gravitational lensing effects associated with rotating black holes within the framework of loop quantum gravity. Utilizing the Gauss-Bonnet theorem as extended by Ono et al., we compute the light deflection angle in the weak field limit for a lens that is finitely distanced from both the source and the observer. Our findings indicate that the weak deflection angle for rotating black holes in LQG is smaller than that observed for the classical Kerr black holes, albeit with minimal deviations. In the strong field limit, we determine the photon sphere radius, the light deflection angle, and lensing observables, including the image position θ∞, angular separation s, magnification rmag, and temporal delays among various relativistic images. By considering supermassive black holes, such as Sgr A* and M87*, within the LQG framework, we calculate these observables and investigate the influence of the quantum parameter Aλ on them, compared with the Kerr black hole outcomes. Our comparative analysis reveals that the image position θ∞ and separation s for Sgr A* consistently exceed those for M87*, whereas M87* exhibits considerably greater time delays than Sgr A*. These distinctions could be important in differentiating between rotating black holes in LQG and classical Kerr black holes in future astronomical observations.

Many previous works have studied gravitational lensing effects from Loop Quantum Gravity. So far, gravitational lensing effects from Loop Quantum Gravity have only been studied by choosing large quantum parameters much larger than the Planck scale. However, by construction, the quantum parameters of the effective models of Loop Quantum Gravity are usually related to the Planck length and, thus, are extremely small. In this work, by strictly imposing the quantum parameters as initially constructed, we study the true quantum corrections of gravitational lensing effects by five effective black hole models of Loop Quantum Gravity. Our study reveals several interesting results, including the different scales of quantum corrections displayed by each model and the connection between the quantum correction of deflection angles and the quantum correction of the metric. Observables related to the gravitational lensing effect are also obtained for all models in the case of SgrA* and M87*.

Integrating loop quantum gravity with classical gravitational collapse models offers an effective solution to the black hole singularity problem and predicts the formation of a white hole in the later stages of collapse. Furthermore, the quantum extension of Kruskal spacetime indicates that white holes may convey information about earlier companion black holes. Photons emitted from the accretion disks of these companion black holes enter the black hole, traverse the highly quantum region, and then re-emerge from white holes in our universe. This process enables us to observe images of the companion black holes’ accretion disks, providing insights into quantum gravity. In our study, we successfully obtained these accretion disk images. Our results indicate that these accretion disk images are confined within a circle with a radius equal to the critical impact parameter, while traditional accretion disk images are typically located outside this circle. As the observational angle increases, the accretion disk images transition from a ring shape to a shell-like shape. Furthermore, the positional and width characteristics of these accretion disk images are opposite to those of traditional accretion disk images. These findings provide valuable references for astronomical observations aimed at validating the investigated quantum gravity model.

A hyperlink is a finite set of non-intersecting simple closed curves in R 4 ≡ R × R 3 , and each curve is either a matter or geometric loop. We consider an equivalence class of such hyperlinks, up to time-like isotopy, preserving time-ordering. Using an equivalence class and after coloring each matter component loop with an irreducible representation of s u (2) × su (2) , we can define its Wilson loop observable using an Einstein–Hilbert action, which is now thought of as a functional acting on the set containing equivalence classes of hyperlink. Construct a vector space using these functionals, which we now term as quantum states. To make it into a Hilbert space, we need to define a counting probability measure on the space containing equivalence classes of hyperlinks. In our previous work, we defined area, volume and curvature operators, corresponding to given geometric objects like surface and a compact solid spatial region. These operators act on the quantum states and, by deliberate construction of the Hilbert space, are self-adjoint and possibly unbounded operators. Using these operators and Einstein's field equations, we can proceed to construct a quantized stress operator and also a Hamiltonian constraint operator for the quantum system. We will also use the area operator to derive the Bekenstein entropy of a black hole. In the concluding section, we will explain how loop quantum gravity predicts the existence of gravitons, implies causality and locality in quantum gravity and formulates the principle of equivalence mathematically in its framework. [ABSTRACT FROM AUTHOR]

We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, with one that acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian for the theory. In previous papers, we studied the theory for large values of the radial coordinate, i.e., far away from any black hole or star that may be present. This makes the calculations considerably more tractable. We have shown that in the asymptotic region, the theory admits a large family of quantum vacua for quantum matter fields coupled to quantum gravity, as is expected from the well-known results of quantum field theory on classical curved space-time. Here, we study perturbative corrections involving terms that we neglected in our previous work. Using the time-dependent perturbation theory, we show that the states that represent different possible vacua are essentially stable. This ensures that one recovers from a totally quantized gravitational theory coupled to matter the standard behavior of a matter quantum field theory plus low probability transitions due to gravity between particles that differ at most by a small amount of energy. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the semi-classical gravitational wave corrections to Gauss's law and obtain an explicit solution for the electromagnetic potential. The gravitational wave perturbs the Coulomb potential with a function that propagates it to the asymptotics. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the corrections to the photon orbits of a nonrotating black hole due to semiclassical fluctuations of the metric. It is found that the photon orbit impact parameter differences with the critical impact parameter become of the order of the semiclassical fluctuations. We calculate the effect of the semiclassical fluctuations on the photon orbits and show that instead of circulating the black hole infinite number of times at the critical orbit, the photons bounce off the semiclassical geometry. [ABSTRACT FROM AUTHOR]

Vacuum spherically symmetric loop quantum gravity in the midi-superspace approximation using inhomogeneous horizon-penetrating slices has been studied for a decade, and it has been noted that the singularity is eliminated. It is replaced by a region of high curvature and potentially large quantum fluctuations. It was recently pointed out that the effective semiclassical metric implies the existence of a shell of matter which violates energy conditions in regions where the curvature is largest. Here, we propose an alternative way of treating the problem that is free from the shells. The ambiguity in the treatment is related with the existence of new observables in the quantum theory that characterize the area excitations, and how the counterpart of diffeomorphisms in the discrete quantum theory is mapped to the continuum semiclassical picture. The resulting spacetime in the high curvature region inside the horizon is approximated by a metric of the type of the Simpson–Visser wormhole and it connects the black hole interior to a white hole in a smooth manner. [ABSTRACT FROM AUTHOR]

Loop quantum gravity (LQG) is a quantization program for gravity based on the principles of QFT and general covariance of general relativity. Quantum states of LQG describe gravitational excitations based on graphs embedded in a spatial slice of spacetime. We show that, under certain assumptions on the class of diffeomorphisms, the space of diffeomorphism invariant states carries a Fock space structure. The role of one-particle excitations for this structure is played by the diffeomorphism invariant states based on graphs with a single (linked) component. This means, however, that a lot of the structure of the diffeomorphism invariant Hilbert space remains unresolved by this structure. We show how the Fock structure allows to write at least some condensate states of group field theory as diffeomorphism invariant coherent states of LQG in a precise sense. We also show how to construct other interesting states using this Fock structure. We finally explore the quantum geometry of single- and multi-particle states and tentatively observe some resemblance to geometries with a single or multiple components, respectively. [ABSTRACT FROM AUTHOR]

The black hole information puzzle can be resolved if two conditions are met. The first is that the information about what falls inside a black hole remains encoded in degrees of freedom that persist after the black hole completely evaporates. These degrees of freedom should be capable of purifying the information. The second is if these purifying degrees of freedom do not significantly contribute to the system's energy, as the macroscopic mass of the initial black hole has been radiated away as Hawking radiation to infinity. The presence of microscopic degrees of freedom at the Planck scale provides a natural mechanism for achieving these two conditions without running into the problem of the large pair-creation probabilities of standard remnant scenarios. In the context of Hawking radiation, the first condition implies that correlations between the in and out Hawking partner particles need to be transferred to correlations between the microscopic degrees of freedom and the out partners in the radiation. This transfer occurs dynamically when the in partners reach the singularity inside the black hole, entering the UV regime of quantum gravity where the interaction with the microscopic degrees of freedom becomes strong. The second condition suggests that the conventional notion of the vacuum's uniqueness in quantum field theory should fail when considering the full quantum gravity degrees of freedom. In this paper, we demonstrate both key aspects of this mechanism using a solvable toy model of a quantum black hole inspired by loop quantum gravity. [ABSTRACT FROM AUTHOR]

The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin foam models of quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin foam model and discuss the role of the causal structure in the reconstruction of a semiclassical space–time geometry.

The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In the framework of loop quantum gravity, the scalar constraint is promoted to two versions of well-defined operators in a suitable Hilbert space of the coupled system, such that the physical Hamiltonian can become some symmetric operators. By the deparametrized form, a general expression of the solutions to either of the quantum scalar constraints is obtained, and the observables on the space of solutions can be constructed. Thus, the Dirac quantization procedure can be fully carried out in loop quantum gravity by this system.

Taking the advantages of loop quantum gravity (LQG), the quasinormal mode frequency spectrum of black holes is studied with the first law of thermodynamics of black holes by calculating the tunneling rate. With the minimum event horizon area interval given by LQG, our results show that one group of the quasinormal mode spectrum for Kerr–Newman black hole depends only on the outer horizon parameters of the black hole. Choosing the minimum spin properly, we derive the quasinormal mode completely consistent with the present results. More importantly, our results show that the quasinormal modes of black holes should have a series of separated frequency spectra, which further proves that the space-time of black holes is quantized. [ABSTRACT FROM AUTHOR]

Effective models of quantum black holes inspired by loop quantum gravity (LQG) have had success in resolving the classical singularity with polymerisation procedures and by imposing the LQG area gap as a minimum area. The singularity is replaced by a hypersurface of transition from black to white holes, and a recent example is the Ashtekar, Olmedo and Singh (AOS) model for a Schwarzschild black hole. More recently, a one-parameter model, with equal masses for the black and white solutions, was suggested by Alonso-Bardaji, Brizuela and Vera (ABBV). An interesting feature of their quantisation is that the angular part of the metric retains its classical form and the horizon area is therefore the same as in the classical theory. In the present contribution we solve the dynamical equations derived from the ABBV effective Hamiltonian and, by applying the AOS minimal area condition, we obtain the scaling of the polymerisation parameter with the black hole mass. We then show that this effective model can also describe Planck scale black holes, and that the curvature and quantum corrections at the horizon are small even at this scale. By generating the exterior metric through a phase rotation in the dynamical variables, we also show that, for an asymptotic observer, the Kretschmann scalar is the same as in the classical Schwarzschild solution, but with a central mass screened by the quantum fluctuations. [ABSTRACT FROM AUTHOR]

In recent decades, there has been growing interest in the quantization of black holes using techniques developed in loop quantum cosmology. Due to the quantum geometry effect, the resulting quantum-corrected black hole provides non-singular models. The quantization scheme can be roughly divided into four types: (1) the μ 0 scheme, (2) the μ ¯ scheme, (3) the generalized μ 0 scheme, and (4) the quantum collapsing model. This paper provides an introduction of the loop quantum black hole model, a summary of the progress made in this field, as well as the quantum effective dynamics and physical applications of these models. [ABSTRACT FROM AUTHOR]

Recent work has shown that local supersymmetry on a spacetime boundary in N -extended AdS supergravity in chiral variables implies coupling to a boundary OSp (N | 2) C super Chern–Simons theory. Consequently there has been a proposal to define and calculate the entropy S for the boundary, in the supersymmetric version of loop quantum gravity, for the minimal case N = 1 , via this super Chern–Simons theory. We give an overview of how supergravity can be treated in loop quantum gravity. We review the calculation of the dimensions of the quantum state spaces of UOSp (1 | 2) super Chern–Simons theory with punctures, and its analytical continuation, for the fixed quantum super area of the surface, to OSp (1 | 2) C . The result is S = a H / 4 for large (super) areas. Lower order corrections can also be determined. We begin also a discussion of the statistical mechanics of the surface degrees of freedom by calculating the grand canonical partition function at zero chemical potential. This is a new result. [ABSTRACT FROM AUTHOR]

We present a simplicial model for gravity written in terms of a discretized Lorentz connection and a discretized tetrad field. The continuum limit of its action is Holst's action for general relativity. With the intention of using it to construct spin foam modes for quantum gravity, we write two other equivalent models written in terms of a discretized and constrained B field. The differences between our model and existing models are most likely inessential in the sense that a quantization would lead to equivalent quantum theories in the Wilsonian continuum limit. Nevertheless, we mention two features leading to possible advantages: Curvature degrees of freedom are described at the level of each 4-simplex. Our model offers a picture of bulk geometry leading to actions for matter couplings that split as a sum over 4-simplices. [ABSTRACT FROM AUTHOR]

In this article, we have studied the dynamics of electrically and magnetically charged particles in the spacetime of loop quantum gravity-corrected Schwarzschild black hole (LQGBH). We consider the loop quantum gravity (LQG) immersed in an external asymptotically uniform magnetic field. The effects of LQG spacetime on dynamics of the particles is studied. We have discussed the circular orbits of the particles about the central object and studied the dependence of the inner stable circular orbits (ISCOs) on the magnetic coupling parameter and the black hole parameters. The synchrotron radiations coming out of the charged particle (accelerated by electromagnetic forces Coulomb and Lorentz) in the surrounding of the magnetized LQGBH is analysed. We have also studied the effects of LQG parameters on the specific angular momentum, energy and ISCOs. We calculated the minimum energy and angular momentum of the magnetized particles required to move in the ISCO. We did this analysis by first calculating the magnetic coupling parameter of the LQGBH spacetime. We have also investigated the collision of neutral, electrically and magnetically charged particles and their centre of mass energy. It is observed that magnetic field around black hole increases the particle acceleration around LQGBH. [ABSTRACT FROM AUTHOR]

We study the behavior of the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam amplitude with homogeneous boundary data, under a graph refinement going from five to twenty boundary tetrahedra. This can be interpreted as a wave function of the Universe, for which we compute boundary geometrical operators, correlation functions, and entanglement entropy. The numerical calculation is made possible by adapting the Metropolis-Hastings algorithm, along with recently developed computational methods appropriate for the deep quantum regime. We confirm that the transition amplitudes are stable against such refinement. We find that the average boundary geometry does not change, but the new degrees of freedom correct the quantum fluctuations of the boundary and the correlations between spatial patches. The expectation values are compatible with their geometrical interpretation and the correlations between neighboring patches decay when computed across different spinfoam vertices. [ABSTRACT FROM AUTHOR]

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 objects. We show that the frequency and energy density of this radiation, which are measurable in principle, suffice to estimate the mass of the parent holes and the remnant density, if the age of the population is known. [ABSTRACT FROM AUTHOR]

We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, with one that acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian for the theory. In previous papers, we studied the theory for large values of the radial coordinate, i.e., far away from any black hole or star that may be present. This makes the calculations considerably more tractable. We have shown that in the asymptotic region, the theory admits a large family of quantum vacua for quantum matter fields coupled to quantum gravity, as is expected from the well-known results of quantum field theory on classical curved space-time. Here, we study perturbative corrections involving terms that we neglected in our previous work. Using the time-dependent perturbation theory, we show that the states that represent different possible vacua are essentially stable. This ensures that one recovers from a totally quantized gravitational theory coupled to matter the standard behavior of a matter quantum field theory plus low probability transitions due to gravity between particles that differ at most by a small amount of energy.

In this paper, we discuss the semi-classical gravitational wave corrections to Gauss’s law and obtain an explicit solution for the electromagnetic potential. The gravitational wave perturbs the Coulomb potential with a function that propagates it to the asymptotics.

The Barbero–Immirzi parameter, (γ), is introduced in loop quantum gravity (LQG), whose physical significance is still the biggest open question because of its profound traits. In some cases, it is real valued, while it is complex valued in other cases. This parameter emerges in the process of denoting a Lorentz connection with a non-compact group SO(3,1) in the form of a complex connection with values in a compact group of rotations, either SO(3) or SU(2). Initially, it appeared in the Ashtekar variables. Fernando Barbero proposed its possibility for inclusion within formalism. Its present value is fixed by counting micro states in loop quantum gravity and matching with the semi-classical black hole entropy computed by Stephen Hawking. This parameter is used to count the size of the quantum of area in Planck units. Until the discovery of the spectrum of the area operator in LQG, its significance remained unknown. However, its complete physical significance is yet to be explored. In the present paper, an introduction to the Barbero–Immirzi parameter in LQG, a timeline of this research area, and various proposals regarding its physical significance are given.

With the discovery of gravitational waves, the search for the quantum of gravity, the graviton, is imminent. We discuss the current status of the bounds on graviton mass from experiments as well as the theoretical understanding of these particles. We provide an overview of current experiments in astrophysics such as the search for Hawking radiation in gamma-ray observations and neutrino detectors, which will also shed light on the existence of primordial black holes. Finally, the semiclassical corrections to the image of the event horizon are discussed. [ABSTRACT FROM AUTHOR]

The black hole information puzzle can be resolved if two conditions are met. The first is that the information about what falls inside a black hole remains encoded in degrees of freedom that persist after the black hole completely evaporates. These degrees of freedom should be capable of purifying the information. The second is if these purifying degrees of freedom do not significantly contribute to the system’s energy, as the macroscopic mass of the initial black hole has been radiated away as Hawking radiation to infinity. The presence of microscopic degrees of freedom at the Planck scale provides a natural mechanism for achieving these two conditions without running into the problem of the large pair-creation probabilities of standard remnant scenarios. In the context of Hawking radiation, the first condition implies that correlations between the in and out Hawking partner particles need to be transferred to correlations between the microscopic degrees of freedom and the out partners in the radiation. This transfer occurs dynamically when the in partners reach the singularity inside the black hole, entering the UV regime of quantum gravity where the interaction with the microscopic degrees of freedom becomes strong. The second condition suggests that the conventional notion of the vacuum’s uniqueness in quantum field theory should fail when considering the full quantum gravity degrees of freedom. In this paper, we demonstrate both key aspects of this mechanism using a solvable toy model of a quantum black hole inspired by loop quantum gravity.

The Barbero–Immirzi parameter, (γ), is introduced in loop quantum gravity (LQG), whose physical significance is still the biggest open question because of its profound traits. In some cases, it is real valued, while it is complex valued in other cases. This parameter emerges in the process of denoting a Lorentz connection with a non-compact group SO(3,1) in the form of a complex connection with values in a compact group of rotations, either SO(3) or SU(2). Initially, it appeared in the Ashtekar variables. Fernando Barbero proposed its possibility for inclusion within formalism. Its present value is fixed by counting micro states in loop quantum gravity and matching with the semi-classical black hole entropy computed by Stephen Hawking. This parameter is used to count the size of the quantum of area in Planck units. Until the discovery of the spectrum of the area operator in LQG, its significance remained unknown. However, its complete physical significance is yet to be explored. In the present paper, an introduction to the Barbero–Immirzi parameter in LQG, a timeline of this research area, and various proposals regarding its physical significance are given. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate the consequences of loop quantum gravitational modifications on the formation of naked singularities. The loop quantum gravitational effects will be incorporated in the collapsing system using gravity's rainbow. This will be done by using rainbow functions, which are constructed from loop quantum gravitational modifications to the energy momentum dispersion. It will be observed that this modification will prevent the formation of naked singularity. Thus, such a modification can ensure that the weak cosmic censorship hypothesis will hold for any collapsing system [ABSTRACT FROM AUTHOR]

We propose a new polymerization scheme for scalar fields coupled to gravity. It has the advantage of being a (non-bijective) canonical transformation of the fields, and therefore ensures the covariance of the theory. We study it in detail in spherically symmetric situations and compare to other approaches. [ABSTRACT FROM AUTHOR]

To date, a mathematically consistent construction of effective rotating black hole models in the context of Loop Quantum Gravity (LQG) is still lacking. In this work, we start with the assumption that rotating LQG black hole metrics can be effectively obtained using Newman–Janis Algorithm. Then, based on a few extra fair assumptions on the seed metric functions, we make a conjecture on what a rotating LQG black hole would generically look like. Our general arguments and conclusions can be supported by some known specific examples in the literature. [ABSTRACT FROM AUTHOR]

We review, as well as provide some new results regarding the study of the structure of spacetime and the singularity in the interior of the Schwarzschild black hole in both loop quantum gravity and generalized uncertainty principle approaches, using congruences and their associated expansion scalar and the Raychaudhuri equation. We reaffirm previous results that in loop quantum gravity, in all three major schemes of polymer quantization, the expansion scalar, Raychaudhuri equation and the Kretschmann scalar remain finite everywhere in the interior. In the context of the eneralized uncertainty principle, we show that only two of the four models we study lead to similar results. These two models have the property that their algebra is modified by configuration variables rather than the momenta. [ABSTRACT FROM AUTHOR]

Recent work has shown that local supersymmetry on a spacetime boundary in N-extended AdS supergravity in chiral variables implies coupling to a boundary OSp(N|2)C super Chern–Simons theory. Consequently there has been a proposal to define and calculate the entropy S for the boundary, in the supersymmetric version of loop quantum gravity, for the minimal case N=1, via this super Chern–Simons theory. We give an overview of how supergravity can be treated in loop quantum gravity. We review the calculation of the dimensions of the quantum state spaces of UOSp(1|2) super Chern–Simons theory with punctures, and its analytical continuation, for the fixed quantum super area of the surface, to OSp(1|2)C. The result is S=aH/4 for large (super) areas. Lower order corrections can also be determined. We begin also a discussion of the statistical mechanics of the surface degrees of freedom by calculating the grand canonical partition function at zero chemical potential. This is a new result.

In recent decades, there has been growing interest in the quantization of black holes using techniques developed in loop quantum cosmology. Due to the quantum geometry effect, the resulting quantum-corrected black hole provides non-singular models. The quantization scheme can be roughly divided into four types: (1) the μ0 scheme, (2) the μ¯ scheme, (3) the generalized μ0 scheme, and (4) the quantum collapsing model. This paper provides an introduction of the loop quantum black hole model, a summary of the progress made in this field, as well as the quantum effective dynamics and physical applications of these models.

In this paper, we explore gravitational lensing effects associated with rotating black holes within the framework of loop quantum gravity. Utilizing the Gauss-Bonnet theorem as extended by Ono et al., we compute the light deflection angle in the weak field limit for a lens that is finitely distanced from both the source and the observer. Our findings indicate that the weak deflection angle for rotating black holes in LQG is smaller than that observed for the classical Kerr black holes, albeit with minimal deviations. In the strong field limit, we determine the photon sphere radius, the light deflection angle, and lensing observables, including the image position θ ∞ , angular separation s , magnification r mag , and temporal delays among various relativistic images. By considering supermassive black holes, such as Sgr A* and M87*, within the LQG framework, we calculate these observables and investigate the influence of the quantum parameter A λ on them, compared with the Kerr black hole outcomes. Our comparative analysis reveals that the image position θ ∞ and separation s for Sgr A* consistently exceed those for M87*, whereas M87* exhibits considerably greater time delays than Sgr A*. These distinctions could be important in differentiating between rotating black holes in LQG and classical Kerr black holes in future astronomical observations. [ABSTRACT FROM AUTHOR]

This paper presents a novel path integral formalism for Einstein's theory of gravitation from the viewpoint of optimal control theory. Despite its close connection to the well-known variational principle of physicists, optimal control turns out to be more general. Within this context, a Lagrangian which is different from the Einstein-Hilbert Lagrangian is defined. Einstein's field equations are recovered exactly with variations of the new action functional. The quantum theory is obtained using Ashtekar variables and the loop scalar product. As an illustrative example, the tunneling process of a black hole into another black hole or into a white hole is investigated with a toy model. [ABSTRACT FROM AUTHOR]

Spin foam theory is a concrete framework for quantum gravity where numerical calculations of transition amplitudes are possible. Recently, the field became very active, but the entry barrier is steep, mainly because of its unusual language and notions scattered around the literature. This paper is a pedagogical guide to spin foam transition amplitude calculations. We show how to write an EPRL-FK transition amplitude, from the definition of the 2-complex to its numerical implementation using sl2cfoam-next. We guide the reader using an explicit example balancing mathematical rigor with a practical approach. We discuss the advantages and disadvantages of our strategy and provide a novel look at a recently proposed approximation scheme. [ABSTRACT FROM AUTHOR]

Since Einstein’s failure to define a Grand Unified Theory, physicists have pursued a comprehensive theory explaining nature, a Theory of Everything. But because General Relativity, Quantum Field Theory, and Cosmology have little in common, defining one theory is an imposing task, having eluded the best scientists for ninety years. So are we close to defining a Theory of Everything? This analysis, after defining requirements (which must include initial conditions), identifies four possible options for a Theory of Everything. Quotes from prominent physicists express divergent views on each alternative.The leading proposal for a Theory of Everything is String Theory, which has possible issues. It requires supersymmetry, has extra compacted dimensions, and is background-dependent. A second less comprehensive theory is Loop Quantum Gravity, which emphases background-independence based on discrete quantum space. Explaining how theories define relationships between spacetime, quantum space, quantum time, and quantum gravity, positions the role of background-independence in proposed theories. If supersymmetry and extra dimensions are discovered, String Theory or a modified String Theory integrated with Loop Quantum Gravity, may be the option. Or, possibly a radically new theory might be developed. Or, as the last option considers, the answer to the question — Does a Theory of Everything exist? — may be no; if so, nature will always be a mystery.

With the discovery of gravitational waves, the search for the quantum of gravity, the graviton, is imminent. We discuss the current status of the bounds on graviton mass from experiments as well as the theoretical understanding of these particles. We provide an overview of current experiments in astrophysics such as the search for Hawking radiation in gamma-ray observations and neutrino detectors, which will also shed light on the existence of primordial black holes. Finally, the semiclassical corrections to the image of the event horizon are discussed.

The authors previously introduced a diffeomorphism-invariant definition of a homogeneous and isotropic sector of loop quantum gravity (LQG), along with a program to embed loop quantum cosmology (LQC) into it. The present paper works out that program in detail for the simpler, but still physically non-trivial, case where the target of the embedding is the homogeneous, but not isotropic, Bianchi I model. The diffeomorphism-invariant conditions imposing homogeneity and isotropy in the full theory reduce to conditions imposing isotropy on an already homogeneous Bianchi I spacetime. The reduced conditions are invariant under the residual diffeomorphisms still allowed after gauge fixing the Bianchi I model. We show that there is a unique embedding of the quantum isotropic model into the homogeneous quantum Bianchi I model that (a) is covariant with respect to the actions of such residual diffeomorphisms, and (b) intertwines both the (signed) volume operator and at least one directional Hubble rate. That embedding also intertwines all other operators of interest in the respective loop quantum cosmological models, including their Hamiltonian constraints. It thus establishes a precise equivalence between dynamics in the isotropic sector of the Bianchi I model and the quantized isotropic model, and not just their kinematics. We also discuss the adjoint relationship between the embedding map defined here and a projection map previously defined by Ashtekar and Wilson-Ewing. Finally, we highlight certain features that simplify this reduced embedding problem, but which may not have direct analogues in the embedding of homogeneous and isotropic LQC into full LQG. [ABSTRACT FROM AUTHOR]

The quasi-local notion of an isolated horizon is employed to study the entropy of black holes without any particular symmetry in loop quantum gravity. The idea of characterizing the shape of a horizon by a sequence of local areas is successfully applied in the scheme to calculate the entropy by the S O(1, 1) BF boundary theory matching loop quantum gravity in the bulk. The generating function for calculating the microscopical degrees of freedom of a given isolated horizon is obtained. Numerical computations of small black holes indicate a new entropy formula containing the quantum correction related to the partition of the horizon. Further evidence shows that, for a given horizon area, the entropy decreases as a black hole deviates from the spherically symmetric one, and the entropy formula is also well suitable for big black holes. [ABSTRACT FROM AUTHOR]

It is argued that certain quantum theories of gravity — string theory, loop quantum gravity, non‐commutative field theory — do not include spacetime as part of their fundamental ontology. There is a concern in the literature that theories of this kind are physically opaque and empirically incoherent. In this paper, I clarify and amend Huggett and Wüthrich's argument against these claims. Whereas the content of this paper centres on the disappearance and re‐emergence of spacetime in quantum gravity, much of the philosophical work centres more generally on issues of (emergent) ontology and how this ontology can be extracted from formal theories, the role of formal derivations in justifying ontological relations, the nature of Kuhnian revolutions, and the application of these revolutions to quantum gravity. [ABSTRACT FROM AUTHOR]