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Two remarkable facts about Jackiw–Teitelboim (JT) two-dimensional dilaton-gravity have been recently uncovered: this theory is dual to an ensemble of quantum mechanical theories; and such ensembles are described by a random matrix model which itself may be regarded as a special (large matter-central-charge) limit of minimal string theory. This work addresses this limit, putting it in its broader matrix-model context; comparing results between multicritical models and minimal strings (i.e. changing in-between multicritical and conformal backgrounds); and in both cases making the limit of large matter-central-charge precise (as such limit can also be defined for the multicritical series). These analyses are first done via spectral geometry, at both perturbative and nonperturbative levels, addressing the resurgent large-order growth of perturbation theory, alongside a calculation of nonperturbative instanton-actions and corresponding Stokes data. This calculation requires an algorithm to reach large-order, which is valid for arbitrary two-dimensional topological gravity. String equations—as derived from the Gel'fand–Dikii construction of the resolvent—are analyzed in both multicritical and minimal string theoretic contexts, and studied both perturbatively and nonperturbatively (always matching against the earlier spectral-geometry computations). The resulting solutions, as described by resurgent transseries, are shown to be resonant. The large matter-central-charge limit is addressed—in the string-equation context—and, in particular, the string equation for JT gravity is obtained to next derivative-orders, beyond the known genus-zero case (its possible exact-form is also discussed). Finally, a discussion of gravitational perturbations to Schwarzschild-like black hole solutions in these minimal-string models, regarded as deformations of JT gravity, is included—alongside a brief discussion of quasinormal modes. [ABSTRACT FROM AUTHOR]

An interesting phenomenological consequence of Λ varying gravity theories inspired by quantum gravity models is reported. The treatment in the present work is quite general and applicable to several different actions with Λ varying, especially those used in RG approaches to quantum gravity. An effective gravitational action with a scale varying cosmological constant, Λ, which depends on the system's characteristics, like the length and the energy density, is the key feature. If the system is an astrophysical object, like a cluster of galaxies, a black hole, etc, non-negligible corrections arise to several observable quantities. Distinctive footprints could refer to luminosity distance and strong/weak lensing measurements, among others. The present study focuses on the SNIa luminosity distance observable. [ABSTRACT FROM AUTHOR]

The end state of Hawking evaporation of a black hole is uncertain. Some candidate quantum gravity theories, such as loop quantum gravity and asymptotic safe gravity, hint towards Planck sized remnants. If so, the Universe might be filled with remnants of tiny primordial black holes, which formed with mass M < 10 9 g. A unique scenario is the case of M ∼ 5 × 10 5 g, where tiny primordial black holes reheat the Universe by Hawking evaporation and their remnants dominate the dark matter (DM). Here, we point out that this scenario leads to a cosmological gravitational wave signal at frequencies ∼100 Hz. Finding such a particular gravitational wave signature with, e.g. the Einstein telescope, would suggest black hole remnants as DM. [ABSTRACT FROM AUTHOR]

An outstanding open issue in our quest for physics beyond Einstein is the unification of general relativity (GR) and quantum physics. Loop quantum gravity (LQG) is a leading approach toward this goal. At its heart is the central lesson of GR: gravity is a manifestation of spacetime geometry. Thus, the approach emphasizes the quantum nature of geometry and focuses on its implications in extreme regimes—near the big bang and inside black holes—where Einstein's smooth continuum breaks down. We present a brief overview of the main ideas underlying LQG and highlight a few recent advances. This report is addressed to non-experts. [ABSTRACT FROM AUTHOR]

Some quantum gravity theories, like loop quantum gravity, predict that quantum mechanical effects will avoid the formation of a singularity inside a black hole. From the general relativity point of view, this means that the metric will differ from the ones of Schwarzschild or Kerr at least inside the event horizon. If the metric is not that of Schwarzschild or Kerr, the potential of the Regge–Wheeler equation is modified, therefore it is possible to peek inside a black hole using the quasi-normal modes to find out if there is indeed a singularity. We address this problem for a regular Schwartzchild black hole using an effective metric first introduced by Hayward. [ABSTRACT FROM AUTHOR]

We study the 'improved dynamics' for the treatment of spherically symmetric space-times in loop quantum gravity introduced by Chiou et al in analogy with the one that has been constructed by Ashtekar, Pawlowski and Singh for the homogeneous space-times. In this dynamics the polymerization parameter is a well motivated function of the dynamical variables, reflecting the fact that the quantum of area depends on them. Contrary to the homogeneous case, its implementation does not trigger undesirable physical properties. We identify semiclassical physical states in the quantum theory and derive the corresponding effective semiclassical metrics. We then discuss some of their properties. Concretely, the space-time approaches sufficiently fast the Schwarzschild geometry at low curvatures. Besides, regions where the singularity is in the classical theory get replaced by a regular but discrete effective geometry with finite and Planck order curvature, regardless of the mass of the black hole. This circumvents trans-Planckian curvatures that appeared for astrophysical black holes in the quantization scheme without the improvement. It makes the resolution of the singularity more in line with the one observed in models that use the isometry of the interior of a Schwarzschild black hole with the Kantowski–Sachs loop quantum cosmologies. One can observe the emergence of effective violations of the null energy condition in the interior of the black hole as part of the mechanism of the elimination of the singularity. [ABSTRACT FROM AUTHOR]

We present a geometric classification of all spherically symmetric spacetimes that could result from singularity regularization, using a kinematic construction that is both exhaustive and oblivious to the dynamics of the fields involved. Due to the minimal geometric assumptions underlying it, this classification encompasses virtually all modified gravity theories, and any theory of quantum gravity in which an effective description in terms of an effective metric is available. The first noteworthy conclusion of our analysis is that the number of independent classes of geometries that can be constructed is remarkably limited, with no more than a handful of qualitatively different possibilities. But our most remarkable result is that this catalogue of possibilities clearly demonstrates that the degree of internal consistency and the strength of deviations with respect to general relativity are strongly, and positively, correlated. Hence, either quantum fluctuations of spacetime come to the rescue and solve these internal consistency issues, or singularity regularization will percolate to macroscopic (near-horizon) scales, radically changing our understanding of black holes and opening new opportunities to test quantum gravity. [ABSTRACT FROM AUTHOR]

In a previous paper we formulated axisymmetric general relativity in terms of real Ashtekar–Barbero variables. Here we proceed to quantize the theory. We are able to implement Thiemann's version of the Hamiltonian constraint. This provides a 2 + 1 dimensional arena to test ideas for the dynamics of quantum gravity and opens the possibility of quantum studies of rotating black hole spacetimes. [ABSTRACT FROM AUTHOR]

We show that the IR action of the healthy non-projectable Hořava–Lifshitz gravity and its small modification exhibit Lifshitz and hyperscaling violating solutions, respectively, though it does not have the corresponding static black hole solutions. The model may also have an AdS2 � Rd vacuum solution. [ABSTRACT FROM AUTHOR]

We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization of the model and that the singularity inside black holes is resolved. Moreover, we consider an alternative quantization based on a slightly different kinematical Hilbert space. The ambiguity in kinematical spaces stems from how one treats the periodicity of one of the classical variables in these models. The corresponding physical Hilbert spaces solve the diffeomorphism and Hamiltonian constraint but their intrinsic structure is radically different depending on the kinematical Hilbert space one started from. In both cases there are quantum observables that do not have a classical counterpart. However, one can show that at the end of the day, by examining Dirac observables, both quantizations lead to the same physical predictions. [ABSTRACT FROM AUTHOR]

Much attention has been recently devoted to modified theories of gravity, the simplest models of which overcome General Relativity simply by replacing R with F(R) in the Einstein–Hilbert action. Unfortunately, such models typically lack most of the beautiful solutions discovered in Einstein’s gravity. Nonetheless, in F(R) gravity, it has been possible to get at least few black holes, but still we do not know any empty wormhole-like spacetime solution. This paper aims to explain why it is so hard to get such solutions (given that they exist!). Few solutions are derived in the simplest cases, while only an implicit form has been obtained in the non-trivial case. [ABSTRACT FROM AUTHOR]

Using a new tortoise coordinate transformation, we discuss the quantum nonthermal radiation characteristics near an event horizon by studying the Hamilton-Jacobi equation of a scalar particle in curved space-time, and obtain the event horizon surface gravity and the Hawking temperature on that event horizon. The results show that there is a crossing of particle energy near the event horizon. We derive the maximum overlap of the positive and negative energy levels. It is also found that the Hawking temperature of a black hole depends not only on the time, but also on the angle. There is a problem of dimension in the usual tortoise coordinate, so the present results obtained by using a correct-dimension new tortoise coordinate transformation may be more reasonable. [ABSTRACT FROM AUTHOR]

We investigate the entropy counting for black hole horizons in loop quantum gravity (LQG). We argue that the space of 3D closed polyhedra is the classical counterpart of the space of SU(2) intertwiners at the quantum level. Then computing the entropy for the boundary horizon amounts to calculating the density of polyhedra or the number of intertwiners at fixed total area. Following the previous work (Bianchi 2011 Class. Quantum Grav. 28 114006) we dub these the classical and quantum polymer models for isolated horizons in LQG. We provide exact micro-canonical calculations for both models and we show that the classical counting of polyhedra accounts for most of the features of the intertwiner counting (leading order entropy and log-correction), thus providing us with a simpler model to further investigate correlations and dynamics. To illustrate this, we also produce an exact formula for the dimension of the intertwiner space as a density of 'almost-closed polyhedra' [ABSTRACT FROM AUTHOR]

We investigate nonrelativistic quantum mechanics on the discretized half-line, constructing a one-parameter family of Hamiltonians that are analogous to the Robin family of boundary conditions in continuum half-line quantum mechanics. For classically singular Hamiltonians, the construction provides a singularity avoidance mechanism that has qualitative similarities with singularity avoidance encountered in loop quantum gravity. Applications include the free particle, the attractive Coulomb potential, the scale invariant potential and a black hole described in terms of the Einstein-Rosen wormhole throat. The spectrum is analysed by analytic and numerical techniques. In the continuum limit, the full Robin family of boundary conditions can be recovered via a suitable fine-tuning but the Dirichlet-type boundary condition emerges as generic. [ABSTRACT FROM AUTHOR]

The loop quantum dynamics of Kantowski–Sachs spacetime and the interior of higher genus black hole spacetimes with a cosmological constant has some peculiar features not shared by various other spacetimes in loop quantum cosmology. As in the other cases, though the quantum geometric effects resolve the physical singularity and result in a non-singular bounce, after the bounce a spacetime with small spacetime curvature does not emerge in either the subsequent backward or the forward evolution. Rather, in the asymptotic limit the spacetime manifold is a product of two constant curvature spaces. Interestingly, though the spacetime curvature of these asymptotic spacetimes is very high, their effective metric is a solution to Einstein’s field equations. Analysis of the components of the Ricci tensor shows that after the singularity resolution, the Kantowski–Sachs spacetime leads to an effective metric which can be interpreted as the ‘charged’ Nariai, while the higher genus black hole interior can similarly be interpreted as an anti Bertotti–Robinson spacetime with a cosmological constant. These spacetimes are ‘charged’ in the sense that the energy–momentum tensor that satisfies Einstein’s field equations is formally the same as the one for the uniform electromagnetic field, albeit it has a purely quantum geometric origin. The asymptotic spacetimes also have an emergent cosmological constant which is different in magnitude, and sometimes even its sign, from the cosmological constant in the Kantowski–Sachs and the interior of higher genus black hole metrics. With a fine tuning of the latter cosmological constant, we show that ‘uncharged’ Nariai, and anti Bertotti–Robinson spacetimes with a vanishing emergent cosmological constant can also be obtained. [ABSTRACT FROM AUTHOR]

Most calculations of black hole entropy in loop quantum gravity indicate a term proportional to the area eigenvalue A with a correction involving the logarithm of A. This violates the additivity of the entropy. An entropy proportional to A, with a correction term involving the logarithm of the classical area k, which is consistent with the additivity of entropy, is derived in both U(1) and SU(2) formulations. [ABSTRACT FROM AUTHOR]

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 during 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. [ABSTRACT FROM AUTHOR]