Related papers: Algebraic approach to quantum gravity IV: applicat…
We continue recent work and formulate the gravitational vacuum Einstein equations over a locally finite spacetime by using the basic axiomatics, techniques, ideas and working philosophy of Abstract Differential Geometry. The whole…
We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framework, the vacuum is peaked on flat connections, and states…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
This paper consists of three steps. In the first, we prove that the Bekenstein-Hawking entropy is the unique expression of black hole entropy. Our proof is constructed in the framework of thermodynamics without any statistical discussion.…
In General Relativity, gravity around a black hole is universally regarded as an attractive force. However, quantum effects may significantly alter this classical picture and thus affect the dynamics of test particles. In this work, we…
Applications to quantum gravity of some results in C*-algebras are developed. We open by describing why algebra may be an integral aspect of quantum gravity. By interpreting the inner automorphisms of a C*-algebra as families of parallel…
The quantum theory of the spherically symmetric gravity in 3+1 dimensions is investigated. The functional measures are explicitly evaluated and the physical state conditions are derived by using the technique developed in two dimensional…
One of the biggest challenges to theoretical physics of our time is to find a background-independent quantum theory of gravity. Today one encounters a profusion of different attempts at quantization, but no fully accepted - or acceptable,…
In general, a global and unique vacuum state cannot be constructed for a curved space. As a remedy, we introduce a curved space background geometry with a Minkowski metric tensor and locally non-zero curvature and torsion. Based on this…
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…
We search for a universal property of quantum gravity. By "universal", we mean the independence from any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on).…
We study new black hole solutions in quantum gravity. We use the Vilkovisky-DeWitt unique effective action to obtain quantum gravitational corrections to Einstein's equations. In full analogy to previous work done for quadratic gravity, we…
It is shown that application of dynamic flows concept in 4-dimensional Euclidean space makes possible to form Minkowski space and to formulate the generalized variational problem of electrodynamics and gravi- dynamics. It is shown that…
If gravity respects quantum mechanics, it is important to identify the essential postulates of a quantum framework capable of incorporating gravitational phenomena. Such a construct likely requires elimination or modification of some of the…
Whereas the nature of dark components in the Universe remains unknown, alternative models of gravity have been developed to offer a geometric explanation to the origin of such components. In this work we use the Minimal Geometric…
In the context of an extended General Relativity theory with boundary terms included, we introduce a new nonlinear quantum algebra involving a quantum differential operator, with the aim to calculate quantum geometric alterations when a…
This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder like deformation in the background of the Kepler problem. In order to accomplish that task, a newtonian spacetime is…
We present an effective theory to describe the quantization of spherically symmetric vacuum in loop quantum gravity. We include anomaly-free holonomy corrections through a canonical transformation of the Hamiltonian of general relativity,…
We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However,…