Loop Quantum Gravity Corrections Research Articles

Holographic bound on area of a compact binary merger remnant

Using concomitantly the generalized second law of black hole thermodynamics and the holographic Bekenstein entropy bound embellished by loop quantum gravity corrections to quantum black hole entropy, we show that the boundary cross sectional area of the postmerger remnant formed from the compact binary merger in gravitational wave detection experiments like GW150914 et seq., by the LIGO-VIRGO collaboration, is bounded from below. This lower bound is more general than the bound obtained from application of Hawking's classical area theorem for black holes, since it does not depend on whether the inspiralling compact binary pair or the postmerger remnant consists of black holes or other exotic compact objects. The derivation of the bound entails an estimate of the entropy of the gravitational waves emitted during the binary merger, which adapts to gravitational waves an extant formalism proposed originally for particle ensembles. The results for the minimal cross sectional area of the merger remnant due to binary compact mergers observed recently by the LIGO-VIRGO collaboration are discussed. While accurate measurement of the mass of the remnant for the binary neutron star merger GW170817 remains a challenge, we provide a proof of principle that for binary neutron star mergers our lower bound on the cross sectional area of the remnant provides an alternative approach to probe the validity of neutron star equations of state, independent of the tidal deformabilities of the components.

Black hole singularity resolution via the modified Raychaudhuri equation in loop quantum gravity

We derive loop quantum gravity corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole and near the classical singularity. We show that the resulting effective equation implies defocusing of geodesics due to the appearance of repulsive terms. This prevents the formation of conjugate points, renders the singularity theorems inapplicable, and leads to the resolution of the singularity for this spacetime.

Black hole collapse and bounce in effective loop quantum gravity

We derive effective equations with loop quantum gravity corrections for the Lemaître–Tolman–Bondi family of space-times, and use these to study quantum gravity effects in the Oppenheimer–Snyder collapse model. For this model, after the formation of a black hole with an apparent horizon, quantum gravity effects become important in the space-time region where the energy density and space-time curvature scalars become comparable to the Planck scale. These quantum gravity effects first stop the collapse of the dust matter field when its energy density reaches the Planck scale, and then cause the dust field to begin slowly expanding. Due to this continued expansion, the matter field will eventually extend beyond the apparent horizon, at which point the horizon disappears and there is no longer a black hole. There are no singularities anywhere in this space-time. In addition, in the limit that edge effects are neglected, we show that the dynamics for the interior of the star of uniform energy density follow the loop quantum cosmology effective Friedman equation for the spatially flat Friedman–Lemaître–Robertson–Walker space-time. Finally, we estimate the lifetime of the black hole, as measured by a distant observer, to be ∼(GM)2/ℓ Pl.

Stability analysis of Einstein’s universe in loop quantum cosmology

A stability analysis of Einstein’s universe in both classical general relativity and semiclassical loop quantum cosmology regimes is presented. The stability properties of the general relativity model are significantly altered due to loop quantum gravity corrections. Comparisons between both dynamical systems are considered on the basis of these modifications. The loop quantum cosmology solutions are restricted to an open universe model [Formula: see text] and represent a cyclic universe. The integrals of motion for both systems are found and their Hamiltonian structure determined.

Constraining LQG Graph with Light Surfaces: Properties of BH Thermodynamics for Mini-Super-Space, Semi-Classical Polymeric BH.

This work participates in the research for potential areas of observational evidence of quantum effects on geometry in a black hole astrophysical context. We consider properties of a family of loop quantum corrected regular black hole (BHs) solutions and their horizons, focusing on the geometry symmetries. We study here a recently developed model, where the geometry is determined by a metric quantum modification outside the horizon. This is a regular static spherical solution of mini-super-space BH metric with Loop Quantum Gravity (LQG) corrections. The solutions are characterized delineating certain polymeric functions on the basis of the properties of the horizons and the emergence of a singularity in the limiting case of the Schwarzschild geometry. We discuss particular metric solutions on the base of the parameters of the polymeric model related to similar properties of structures, the metric Killing bundles (or metric bundles MBs), related to the BH horizons’ properties. A comparison with the Reissner–Norström geometry and the Kerr geometry with which analogies exist from the point of their respective MBs properties is done. The analysis provides a way to recognize these geometries and detect their main distinctive phenomenological evidence of LQG origin on the basis of the detection of stationary/static observers and the properties of light-like orbits within the analysis of the (conformal invariant) MBs related to the (local) causal structure. This approach could be applied in other quantum corrected BH solutions, constraining the characteristics of the underlining LQG-graph, as the minimal loop area, through the analysis of the null-like orbits and photons detection. The study of light surfaces associated with a diversified and wide range of BH phenomenology and grounding MBs definition provides a channel to search for possible astrophysical evidence. The main BHs thermodynamic characteristics are studied as luminosity, surface gravity, and temperature. Ultimately, the application of this method to this spherically symmetric approximate solution provides us with a way to clarify some formal aspects of MBs, in the presence of static, spherical symmetric spacetimes.

Anamorphic quasiperiodic universes in modified and Einstein gravity with loop quantum gravity corrections

The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/aperiodic/fractal/stochastic/(super) cluster/filament/polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such solutions are characterized by nonlinear symmetries of generating functions for generic off-diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi–Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.

Inhomogeneities, loop quantum gravity corrections, constraint algebra and general covariance

Loop quantum gravity corrections, in the presence of inhomogeneities, can lead to a deformed constraint algebra. Such a deformation implies that the effective theory is no longer generally covariant. As a consequence, the geometrical concepts used in the classical theory lose their meaning. In the present paper we propose a method, based on canonical transformation on the phase space of the spherically symmetric effective theory, to systematically recover the classical constraint algebra in the presence of the inverse triad corrections as well as in the presence of the holonomy corrections. We show, by way of explicit example, that this also leads to the recovery of general covariance of the theory in the presence of inverse triad corrections, implying that one can once again use the geometrical concepts to analyze the solutions in the presence of these quantum gravity corrections.Communicated by P Singh

Spherically symmetric Einstein–Maxwell theory and loop quantum gravity corrections

Effects of inverse triad corrections and (point) holonomy corrections, occurring in loop quantum gravity, are considered on the properties of Reissner–Nordström black holes. The version of inverse triad corrections with unmodified constraint algebra reveals the possibility of occurrence of three horizons (over a finite range of mass) and also shows a mass threshold beyond which the inner horizon disappears. For the version with modified constraint algebra, coordinate transformations are no longer a good symmetry. The covariance property of spacetime is regained by using a quantum notion of mapping from phase space to spacetime. The resulting quantum effects in both versions of these corrections can be associated with renormalization of either mass, charge or wavefunction. In neither of the versions, Newton’s constant is renormalized. (Point) Holonomy corrections are shown to preclude the undeformed version of constraint algebra as also a static solution, though time-independent solutions exist. A possible reason for difficulty in constructing a covariant metric for these corrections is highlighted. Furthermore, the deformed algebra with holonomy corrections is shown to imply signature change.

Logarithmic corrections to $$ \mathcal{N} = {4} $$ and $$ \mathcal{N} = {8} $$ black hole entropy: a one loop test of quantum gravity

We compute logarithmic corrections to the entropy of supersymmetric extremal black holes in $$ \mathcal{N} = {4} $$ and $$ \mathcal{N} = {8} $$ supersymmetric string theories and find results in perfect agreement with the microscopic results. In particular these logarithmic corrections vanish for quarter BPS black holes in $$ \mathcal{N} = {4} $$ supersymmetric theories, but has a finite coefficient for 1/8 BPS black holes in the $$ \mathcal{N} = {8} $$ supersymmetric theory. On the macroscopic side these computations require evaluating the one loop determinant of massless fields around the near horizon geometry, and include, in particular, contributions from dynamical four dimensional gravitons propagating in the loop. Thus our analysis provides a test of one loop quantum gravity corrections to the black hole entropy, or equivalently of the AdS 2/CF T 1 correspondence. We also extend our analysis to $$ \mathcal{N} = {2} $$ supersymmetric STU model and make a prediction for the logarithmic correction to the black hole entropy in that theory.

Loop quantum gravity corrections to gravitational wave dispersion

Cosmological tensor perturbations equations are derived for Hamiltonian cosmology based on Ashtekar's formulation of general relativity, including typical quantum gravity effects in the Hamiltonian constraint as they are expected from loop quantum gravity. This translates to corrections of the dispersion relation for gravitational waves. The main application here is the preservation of causality which is shown to be realized due to the absence of anomalies in the effective constraint algebra used.

Radiation equation of state and loop quantum gravity corrections

The equation of state for radiation is derived in a canonical formulation of the electromagnetic field. This allows one to include correction terms expected from canonical quantum gravity and to infer implications to the universe evolution in radiation dominated epochs. Corrections implied by quantum geometry can be interpreted in physically appealing ways, relating to the conformal invariance of the classical equations.

Effective constraints of loop quantum gravity

Within a perturbative cosmological regime of loop quantum gravity corrections to effective constraints are computed. This takes into account all inhomogeneous degrees of freedom relevant for scalar metric modes around flat space and results in explicit expressions for modified coefficients and of higher order terms. It also illustrates the role of different scales determining the relative magnitude of corrections. Our results demonstrate that loop quantum gravity has the correct classical limit, at least in its sector of cosmological perturbations around flat space, in the sense of perturbative effective theory.

Hamiltonian cosmological perturbation theory with loop quantum gravity corrections

Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation and choice of gauges are pointed out. Nevertheless, the treatment is more systematic when correction terms of canonical quantum gravity are to be included. This is done throughout the paper for one example of characteristic modifications expected from loop quantum gravity.