The goal of this review is to present an introduction loop quantum gravity—a background-independent, non-perturbative approach the problem unification general relativity and physics, based on a theory geometry. Our presentation pedagogical. Thus, in addition providing bird's eye view status subject, should also serve as vehicle enter field explore it detail. To aid non-experts, very little assumed beyond elements relativity, gauge theories theory. While essentially self-contained, emphasis...

A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin systematic construction theory geometry. Regulated operators corresponding areas 2-surfaces are introduced and shown be self-adjoint on the underlying (kinematical) Hilbert space states. It that their spectra {\it purely} discrete indicating geometry far from what continuum picture might suggest. Indeed, fundamental excitations 1-dimensional, rather like polymers,...

Applications of Riemannian quantum geometry to cosmology have had notable successes.In particular, the fundamental discreteness underlying has led a natural resolution big bang singularity.However, precise mathematical structure loop and sense in which it implements full quantization program symmetry reduced model not been made explicit.The purpose this paper is address these issues, thereby providing rmer conceptual foundation subject.

A functional calculus on the space of (generalized) connections was recently introduced without any reference to a background metric.It is used continue exploration quantum Riemannian geometry.Operators corresponding volume three-dimensional regions are rigorously.It shown that there two natural regularization schemes, each which leads well-defined operator.Both operators can be completely specified by giving their action states labelled graphs.The final results closely related but differ...

Quantization of diffeomorphism invariant theories connections is studied. A solutions the constraints found. The space equipped with an inner product that shown to satisfy physical reality conditions. This provides, in particular, a quantization Husain-Kucha\v{r} model. main results also pave way other such as general relativity. In Riemannian case (i.e., signature ++++), approach appears contain all necessary ingredients already. Lorentzian case, it will have combined appropriate fashion...

By considering the quantum Oppenheimer-Snyder model in loop cosmology, a new black hole whose metric tensor is suitably deformed Schwarzschild one derived. The effects imply lower bound on mass of produced by collapsing dust ball. For case larger masses where event horizon does form, maximal extension spacetime and its properties are investigated. discussing opposite scenario to Oppenheimer-Snyder, Swiss Cheese obtained with bubble surrounded universe. This analogous cosmology or fecund...

A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a family compact Hausdorff spaces. The procedure then applied to gauge theories carry out the non-linear, connections modulo transformations. This method evaluating functional integrals can be used either in Euclidean path integral approach or Lorentzian canonical approach. number measures discussed are diffeomorphism invariant and therefore interest (the connection...

Quantum geometry (the modern loop quantum gravity involving graphs and spin-networks instead of the loops) provides microscopic degrees freedom that account for black-hole entropy. However, procedure state counting used in literature contains an error number relevant horizon states is underestimated. In our paper a correct method presented. Our results lead to revision subject. It turns out contribution spins greater than 1/2 entropy not negligible. Hence, value Barbero–Immirzi parameter...

Black hole mechanics was recently extended by replacing the more commonly used event horizons in stationary space-times with isolated general (which may admit radiation arbitrarily close to black holes). However, so far detailed analysis has been restricted nonrotating holes (although it incorporated arbitrary distortion, as well electromagnetic, Yang-Mills, and dilatonic charges). We now fill this gap first introducing notion of horizon angular momentum then extending law rotating case.

The notion of isolated horizons is extended to allow for distortion and rotation. Space-times containing a black hole, itself in equilibrium but possibly surrounded by radiation, satisfy these conditions. framework has three types applications: (i) it provides new tools extract physics from strong field geometry; (ii) leads generalization the zeroth first laws hole mechanics sheds light on "origin" law; (iii) serves as point departure entropy calculations nonperturbative quantum gravity.

Geometrical structures intrinsic to non-expanding, weakly isolated and horizons are analyzed compared with which arise in other contexts within general relativity, e.g., at null infinity. In particular, we address detail the issue of singling out preferred normals these required various applications. This work provides powerful tools extract invariant, physical information from numerical simulations near horizon, strong field geometry. While it complements previous analysis laws governing...

The simplicial framework of Engle–Pereira–Rovelli–Livine spin-foam models is generalized to match the diffeomorphism invariant loop quantum gravity. spin-foams are arbitrary linear 2-cell spin-foams. resulting admits all spin-network states gravity, not only those defined by triangulations (or cubulations). In particular, notion embedded we use allows us consider knotting or linking histories. Also main tools, vertex structure and amplitude, naturally an valency case. correspondence between...

..."but we do not have quantum gravity." This phrase is often used when analysis of a physical problem enters the regime in which gravity effects should be taken into account. In fact, there are several models gravitational field coupled to (scalar) fields for quantization procedure can completed using loop techniques. The model present this paper consist scalar field. result has similar structure cosmology models, except that it involves all local degrees freedom because no symmetry...

A bstract We consider three different approaches (by Ashtekar, Bonga and Kesavan; Hoque Virmani; Dobkowski-Ryłko Lewandowski) to investigate gravitational radiation produced by time changing matter source in de Sitter spacetime. All of them lead generalizations the quadrupole formula, however, due gauge conditions choices hypersurfaces, across which energy flux is computed, it nontrivial see that they all coincide, as one would expect from symplectic theory. Each expressions for radiated...

The basic idea of the LQC applies to every spatially homogeneous cosmological model, however only flat (so called k = 0) case has been understood in detail literature thus far.In closed called: k=1) certain technical difficulties have obstacle that stopped development.In this work are overcome, and a new model closed, homogeneous, isotropic universe is constructed.The topology spacelike section assumed be SU(2) or SO(3).Surprisingly, according results achieved paper, two cases can...

In loop quantum cosmology, Friedmann-LeMa\^{\i}tre-Robertson-Walker space-times arise as well-defined approximations to specific geometries. We initiate the development of a theory test scalar fields on these Emphasis is new conceptual ingredients required in transition from classical space-time backgrounds space-times. These include ``relational time'' \`a la Leibniz, emergence Hamiltonian operator field constraint equation, and ramifications fluctuations background geometry resulting...

A bstract In a companion paper [1] we showed that the symmetry group $$ \mathfrak{G} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> </mml:math> of non-expanding horizons (NEHs) is 1-dimensional extension Bondi-Metzner-Sachs \mathfrak{B} <mml:mi>B</mml:mi> at \mathcal{I} <mml:mi>I</mml:mi> + . For each infinitesimal generator , now define charge and flux on NEHs as well perturbed NEHs. The procedure uses covariant phase space framework in presence internal null...

The collapse of a spherically symmetric ball dust has been intensively studied in loop quantum gravity (LQG). From theory, it is possible to recover semiclassical regime through polymerization procedure. In this setting, general solutions the polymerized Einstein field equations (PEFE) will be discussed both for homogeneous interior and exterior cloud. Exterior are particularly interesting since they may lead version Birkhoff's theorem. It seen that if time independence vacuum imposed, there...

The differential structure of the Ashtekar - Isham quantum configuration space canonical gravity allows expression operators, representing various geometrical objects, by compact analytic formulae. In this paper such a formula is presented for Rovelli Smolin volume operator. This operator compared with defined and Lewandowski difference indicated.

The goal of this paper is to introduce a systematic approach spin foams.We define operator foams, that foams labelled by group representations and operators, as our main tool.A set moves we in the allows (among other operations) split faces edges assign each foam contracted operator, using contractions at vertices suitably adjusted face amplitudes.The emergence amplitudes consequence assuming invariance with respect moves.Next, models consider class assumed be symmetric have introduced,...