Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement Gravity versus SU(∞)-QGR

In a previous article we proposed a new model for quantum gravity (QGR) and cosmology, dubbed SU(∞)-QGR. One of the axioms of this model is that Hilbert spaces of the Universe and its subsystems represent the SU(∞) symmetry group. In this framework, the classical spacetime is interpreted as being the parameter space characterizing states of the SU(∞) representing Hilbert spaces. Using quantum uncertainty relations, it is shown that the parameter space—the spacetime—has a 3+1 dimensional Lorentzian geometry. Here, after a review of SU(∞)-QGR, including a demonstration that its classical limit is Einstein gravity, we compare it with several QGR proposals, including: string and M-theories, loop quantum gravity and related models, and QGR proposals inspired by the holographic principle and quantum entanglement. The purpose is to find their common and analogous features, even if they apparently seem to have different roles and interpretations. The hope is that this exercise provides a better understanding of gravity as a universal quantum force and clarifies the physical nature of the spacetime. We identify several common features among the studied models: the importance of 2D structures; the algebraic decomposition to tensor products; the special role of the SU(2) group in their formulation; the necessity of a quantum time as a relational observable. We discuss how these features can be considered as analogous in different models. We also show that they arise in SU(∞)-QGR without fine-tuning, additional assumptions, or restrictions.

Polytopes in all dimensional loop quantum gravity

The Lasserre’s reconstruction algorithm is extended to the D-polytopes with the construction of their shape space. Thus, the areas of d-skeletons $$(1\le d\le D)$$ ( 1 ≤ d ≤ D ) can be expressed as functions of the areas and normal bi-vectors of the (D-1)-faces of D-polytopes. As weak solutions of the simplicity constraints in all dimensional loop quantum gravity, the simple coherent intertwiners are employed to describe semiclassical D-polytopes. New general geometric operators based on D-polytopes are proposed by using the Lasserre’s reconstruction algorithm and the coherent intertwiners. Such kind of geometric operators have expected semiclassical property by the definition. The consistent semiclassical limit with respect to the semiclassical D-polytopes can be obtained for the usual D-volume operator in all dimensional loop quantum gravity by fixing its undetermined regularization factor case by case.

Improved effective dynamics of loop-quantum-gravity black hole and Nariai limit

We propose a new model of the spherical symmetric quantum black hole in the reduced phase space formulation. We deparametrize gravity by coupling to the Gaussian dust which provides the material coordinates. The foliation by dust coordinates covers both the interior and exterior of the black hole. After the spherical symmetry reduction, our model is a 1+1 dimensional field theory containing infinitely many degrees of freedom. The effective dynamics of the quantum black hole is generated by an improved physical Hamiltonian ${\bf H}_\Delta$. The holonomy correction in ${\bf H}_\Delta$ is implemented by the $\bar{\mu}$-scheme regularization with a Planckian area scale $\Delta$ (which often chosen as the minimal area gap in Loop Quantum Gravity). The effective dynamics recovers the semiclassical Schwarzschild geometry at low curvature regime and resolves the black hole singularity with Planckian curvature, e.g. $R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\sim 1/{\Delta}^2$. Our model predicts that the evolution of the black hole at late time reaches the charged Nariai geometry ${\rm dS}_2\times S^2$ with Planckian radii $\sim \sqrt{\Delta}$. The Nariai geometry is stable under linear perturbations but may be unstable by nonperturbative quantum effects. Our model suggests the existence of quantum tunneling of the Nariai geometry and a scenario of black-hole-to-white-hole transition.

ONTOLOGY OF LOOPED QUANTUM GRAVITY. HINGES

Some ontological aspects of the theory of loop quantum gravity are considered. First of all, its possible nature of one of the fundamental objects of theory - the quantum loop - is discussed. In particular, the possible material, geometric and instrumentalist interpretations of this object are briefly considered.

Black Holes, Gravitational Waves and Quantum Gravity

Loop Quantum Gravity is a theory that attempts to describe the quantum mechanics of the gravitational field based on the canonical quantization of General Relativity. According to Loop Quantum Gravity, in a gravitational field, geometric quantities such as area and volume are quantized in terms of the Planck length. In this paper we present the basic ideas for a future, mathematically more rigorous, attempt to combine black holes and gravitational waves using the quantization of geometric quantities introduced by Loop Quantum Gravity.

Non-extensive statistical mechanics and the thermodynamic stability of FRW universe

In this article, we investigate the thermodynamic stability of the FRW universe for two examples, Tsallis entropy and loop quantum gravity, by considering non-extensive statistical mechanics. The heat capacity, free energy and pressure of the universe are obtained. For the Tsallis entropy model, we obtained the constraint for β, namely, 1/2 <β <2. The free energy of a thermal equilibrium universe must be less than zero. We suggest that the reason for the accelerated expansion of the universe is not due to Tsallis entropy. Similar results are obtained for loop quantum gravity. However, since the values of Λ(γ) and q cannot be determined in this model, the results become more subtle than that in the Tsallis entropy model. In addition, we compare the results for the universe with those for a Schwarzschild black hole.

Quasinormal modes of a massive scalar field nonminimally coupled to gravity in the spacetime of self-dual black hole

In this work, we investigate the quasinormal modes for a massive scalar field with a nonminimal coupling with gravity in the spacetime of a loop quantum black hole, known as the self-dual black hole. In this way, we have calculated the characteristic frequencies using the 3rd order WKB approach, where we can verify a strong dependence with the mass of scalar field, the parameter of nonminimal coupling with gravity, and parameters of the loop quantum gravity. From our results, we can check that the self-dual black hole is stable under the scalar perturbations when assuming small values for the parameters. Also, such results tell us that the quasinormal modes assume different values for the cases where the mass of field is null and the nonminimal coupling assumes $$\xi =0$$ ξ = 0 and $$\xi =1/6$$ ξ = 1 / 6 , i.e., a possible breaking of the conformal invariance can be seen in the context of loop quantum black holes.