Ashtekar-Kodama Gravity as a Classical and Quantum Extension of Loop Quantum Gravity

This paper presents a new theory of gravity, called here Ashtekar-Kodama (AK) gravity, which is based on the Ashtekar-Kodama formulation of loop quantum gravity (LQG), yields in the limit the Einstein equations, and in the quantum regime a full renormalizable quantum gauge field theory. The three fundamental constraints (hamiltonian, gaussian and diffeomorphism) were formulated in 3-dimensional spatial form within LQG in Ashtekar formulation using the notion of the Kodama state with positive cosmological constant Λ. We introduce a 4-dimensional covariant version of the 3-dimensional (spatial) hamiltonian, gaussian and diffeomorphism constraints of LQG. We obtain 32 partial differential equations for the 16 variables Emn (E-tensor, inverse densitized tetrad of the metric) and 16 variables Amn (A-tensor, gravitational wave tensor). We impose the boundary condition: for large distance the E-generated metric g(E) becomes the GR-metric g (normally Schwarzschild-spacetime). The theory based on these Ashtekar-Kodama (AK) equations, and called in the following Ashtekar-Kodama (AK-) gravity has the following properties. • For Λ = 0 the AK equations become Einstein equations, A-tensor is trivial (constant), and the E-generated metric g(E) is identical with the GR-metric g. • When the AK-equations are developed into a Λ-power series, the Λ-term yields a gravitational wave equation, which has only at least quadrupole wave solutions and becomes in the limit of large distance r the (normal electromagnetic) wave equation. • AK-gravity, as opposed to GR, has no singularity at the horizon: the singularity in the metric becomes a (very high) peak. • AK-gravity has a limit scale of the gravitational quantum region 39 μm, which emerges as the limit scale in the objective wave collapse theory of Gherardi-Rimini-Weber. In the quantum region, the AK-gravity becomes a quantum gauge theory (AK quantum gravity) with the Lie group extended SU(2) = ε-tensor-group(four generators) as gauge group and a corresponding covariant derivative. • AK quantum gravity is fully renormalizable, we derive its Lagrangian, which is dimensionally renormalizable, the normalized one-graviton wave function, the graviton propagator, and demonstrate the calculation of cross-section from Feynman diagrams.

Counting the Microstates at the Black Hole Horizon and the Immirzi Parameter of Loop Quantum Gravity

Motivated by Bekenstein’s original thought that led him to his famous area-entropy formula for a black hole and by our recent study regarding the black hole dynamics, we identify the appropriate microscopic degrees of freedom in loop quantum gravity that are responsible for the black hole entropy. We achieve consistent results by taking the j = 1/2 edges as dominant and by subjecting these edges to experience quantum fluctuations at the horizon. This also leads to a modification of the value of the Immirzi parameter in the SU(2) framework.

Loop Quantum Gravity Harmonic Oscillator

Attempts to unify Gravity Theory and Quantum Field Theory (QFT) under Loop Quantum Gravity Theory (LQG), are diverse;a dividing line between classical and quantum is sought with Schrödinger cat-state experiments. A Primordial Field Theory-based alternative is presented, and a gravity-based harmonic oscillator developed. With quantum theory applied at micro-scales and gravity theory at meso- and macro-scales, this scale-gap contributes to the conceptual problems associated with Loop Quantum Gravity. Primordial field theory, spanning all scales, is used to conceptually stretch key ideas across this gap. An LQG interpretation of the wave function associated with the oscillator is explained.

Entropy of black holes with arbitrary shapes in loop quantum gravity

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.

Entropy of nonrotating isolated horizons in Lovelock theory from loop quantum gravity

In this paper, the BF theory method is applied to the nonrotating isolated horizons in Lovelock theory. The final entropy matches the Wald entropy formula for this theory. We also confirm the conclusion obtained by Bodendorfer et al. that the entropy is related to the flux operator rather than the area operator in general diffeomorphic-invariant theory.

Ontology of Quantum Gravity

A theory of Quantum Gravity based on Primordial Field Theory is applied to a fundamental particle, the neutron. The result is compared to the current quantum description of the neutron bouncing in a gravitational field. Our quantum gravity theory yields results in agreement with the Q-bounce experimental data, but ontologically different from quantum mechanics. The differences are summarized and imply that this experiment on a fundamental particle has the potential to radically alter the ontology of field theory.

A Number Theoretic Analysis of the Enthalpy, Enthalpy Energy Density, Thermodynamic Volume, and the Equation of State of a Modified White Hole, and the Implications to the Quantum Vacuum Spacetime, Matter Creation and the Planck Frequency

In this paper, we analyze the enthalpy, enthalpy energy density, thermodynamic volume, and the equation of state of a modified white hole. We obtain new possible mathematical connections with some sectors of Number Theory, Ramanujan Recurring Numbers, DN Constant and String Theory, that enable us to extract the quantum geometrical properties of these thermodynamic equations and the implication to the quantum vacuum spacetime geometry of our early universe as they act as the constraints to the nature of quantum gravity of the universe.

Quantum Mechanics Hypothesis of Solar System Structure: Quantum de Broglie Wavelength, LQG Similitude and Slow Bang Theory (SB)

This idea of quantifying the energy of bodies orbiting the Sun is not new. We have identified that quantization applies well if we use the true quantum number associated with the true energy state of rotating bodies. This quantum number is very high for the main bodies or planets (10~70 to 76). However, since quantum energy levels E are very high and ΔE very low we observe that bodies can in practice occupy all orbits. Thus, the current observed stable positions of the bodies are the results of the quantization and the sum of the effects of other perturbative phenomena. To find a quantum state starting with n = 1, we expressed the true integer quantum numbers as a function of that of the planet Mercury and we find an excellent correlation. However, the search for a correlation of prediction of the average orbital radius of bodies using the simple integer number n = 1, 2, 3, 4, 5, 6, 7, … is not excellent for bodies beyond the planet Pluto. Indeed, several trans-Neptunian bodies have similar integer quantum numbers, which poses a problem in the sequence of integer numbers beyond 10. Moreover, it appears that the trans-Neptunian bodies seem to be grouped for many of them according to relatively well-defined bands. The study made it possible to question the de Broglie wavelength of bodies (10~-58 to -65 m). Indeed, with the hypothesis of Planck quantities that would apply to the scale of the universe, it is difficult to conceive that de Broglie wavelengths are less than the Planck length lp. This led to an expression of the modified de Broglie wavelength λm that predicts an asymptotic lower limit value equal to πlp. This modified de Broglie wavelength makes it possible to obtain a better correlation for the prediction of the average orbital radius of bodies. Finally, this modified wavelength of de Broglie made it possible to put into perspective the concept of the quantification of space with the idea of the minimum wavelength associated with photon’s energies during the generation of the energy of the universe according to a model already presented in this review. This modified de Broglie wavelength also makes it possible to imagine that the quantification of the volume of space involves the geometry of the sphere and the cube.

On the improved dynamics approach in loop quantum black holes

In this paper,we consider the B?hmer–Vandersloot(BV)model of loop quantum black holes obtained from the improved dynamics approach.We adopt the Saini–Singh gauge,in which it was found analytically that the BV spacetime is geodesically complete.We show that black/white hole horizons do not exist in this geodesically complete spacetime.Instead,there exists only an infinite number of transition surfaces,which always separate trapped regions from anti-trapped ones.Comments on the improved dynamics approach adopted in other models of loop quantum black holes are also given.

Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology

The covariant entropy bound conjecture is an important hint for the quantum gravity, with several versions available in the literature. For cosmology, Ashtekar and Wilson-Ewing ever show the consistence between the loop gravity theory and one version of this conjecture. Recently, He and Zhang [J. High Energy Phys. 10 (2007) 077] proposed a version for the dynamical horizon of the universe, which validates the entropy bound conjecture for the cosmology filled with perfect fluid in the classical scenario when the universe is far away from the big bang singularity. However, their conjecture breaks down near big bang region. We examine this conjecture in the context of the loop quantum cosmology. With the example of photon gas, this conjecture is protected by the quantum geometry effects as expected.

The Black Hole Spray and the Cosmic Web

We propose that the trapped antimatter in super massive black hole ergoregions acts as detonators that triggers black hole to white hole transitions creating huge BHs explosions that generate BH spray that acts as seeds for new galaxies creation. We propose that by mapping and simulating the cosmic web structure, it may be possible to learn if the universe was created in a single big bang that started a single chain of BH explosions mini-creation event cycles, or alternatively, the BH explosions mini-creation event cycles are uncorrelated spacelike events, and the universe had no single primeval atom beginning. .

Nonexistence of quantum black and white hole horizons in an improved dynamic approach

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.

Immirzi parameter and quasinormal modes in four and higher spacetime dimensions

There is a one-parameter quantization ambiguity in loop quantum gravity, which is called the Immirzi parameter. In this paper, we fix this free parameter by considering the quasinormal mode spectrum of black holes in four and higher spacetime dimensions. As a consequence, our result is consistent with the Bekenstein-Hawking entropy of a black hole. Moreover, we also give a possible quantum gravity explanation of the universal In 3 behavior of the quasinormal mode spectrum.