scholarly journals General Canonical Quantum Gravity Theory and that of the Universe and General Black Hole

2021 ◽  
Author(s):  
C. Huang ◽  
Yong-Chang Huang ◽  
Xinfei Li
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Nonlinear System ◽  
Quantum Gravity ◽  
Canonical Quantization ◽  
Gravity Theory ◽  
Canonical Momentum ◽  
Canonical Quantum Gravity ◽  
The Universe ◽  
Canonical Quantum

This paper gives both a general canonical quantum gravity theory and the general canonical quantum gravity theories of the Universe and general black hole, and discovers the relations reflecting symmetric properties of the standard nonlinear gravitational Lagrangian, which are not relevant to any concrete metric models. This paper concretely shows the general commutation relations of the general gravitational field operators and their zeroth, first, second and third style, respectively, of high order canonical momentum operators for the general nonlinear system of the standard gravitational Lagrangian, and then has finished all the four styles of the canonical quantization of the standard gravity.

scholarly journals Solutions to the Puzzles of Quantum Gravity and General Theory of Quantum Gravity and Quantum Gravity of the Universe and General Black Hole

2021 ◽  
Author(s):  
C. Huang ◽  
Yong-Chang Huang ◽  
Xinfei Li
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
General Theory ◽  
Quantum Gravity ◽  
Lagrange Equation ◽  
Field Theories ◽  
Canonical Momentum ◽  
Gravitational Fields ◽  
Whole Process ◽  
The Universe

This paper gives both the solutions to the puzzles of quantum gravity and a general theory of quantum gravity, further shows quantum gravity of the Universe and general black hole, and discovers their relations reflecting symmetric propertis of the standard nonlinear gravitational Lagrangian, which are not relevant to any concrete metric models. This paper concretely shows the general commutation relations of the general gravitational field operators and their zeroth, first, second and third style, respectively, of high order canonical momentum operators for the general nonlinear system of the standard gravitational Lagrangian, and then has finished all the four styles of the quantization of the standard gravity. No needing, as usual, to solve the Euler-Lagrange equation to complete the whole process of the quantization of the standard gravitational fields, namely, this paper novelly simplifies all the current quantization theories of the standard gravitational fields. So lots of the complex calculations of quantum gravitational field theories up to now can be omitted to make the physical picture clearer, simpler and more easily understanding. Therefore, the solutions to puzzles of quantum gravity are given. Consequently, this paper opens a door to study and give a general theory of the quantum gravitational field don't depending on any concrete metric models.

ARITHMETIC QUANTUM GRAVITY

2010 ◽  
Vol 19 (14) ◽  
pp. 2305-2310 ◽  
Author(s):  
AXEL KLEINSCHMIDT ◽  
HERMANN NICOLAI
Keyword(s):  
Quantum Gravity ◽  
Algebraic Structure ◽  
Complete Resolution ◽  
Quantum Level ◽  
Cosmological Singularity ◽  
Quantum Billiard ◽  
Symmetry Structure ◽  
Canonical Quantum Gravity ◽  
The Universe ◽  
Canonical Quantum

The arithmetic chaos of classical (super)gravity near a spacelike singularity is elevated to the quantum level via the construction of a cosmological quantum billiard system. Its precise formulation, together with its underlying algebraic structure, allows for a general analysis of the wavefunction of the universe near the singularity. We argue that the extension of these results beyond the billiard approximation may provide a concrete mechanism for emergent space as well as new perspectives on several long-standing issues in canonical quantum gravity. The exponentially growing complexity of the underlying symmetry structure could introduce an element of non-computability that effectively "screens" the cosmological singularity from a complete resolution.

scholarly journals Mass spectrum and statistical entropy of the BTZ black hole from canonical quantum gravity

2008 ◽  
Vol 77 (6) ◽  
Author(s):  
Cenalo Vaz ◽  
Sashideep Gutti ◽  
Claus Kiefer ◽  
T. P. Singh ◽  
L. C. R. Wijewardhana
Keyword(s):  
Black Hole ◽  
Mass Spectrum ◽  
Quantum Gravity ◽  
Statistical Entropy ◽  
Btz Black Hole ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum

scholarly journals Canonical quantum gravity on noncommutative space–time

2015 ◽  
Vol 30 (17) ◽  
pp. 1550085 ◽  
Author(s):  
Martin Kober
Keyword(s):  
Gravitational Field ◽  
Quantum Gravity ◽  
Classical Theory ◽  
Star Product ◽  
Space Time ◽  
Noncommutative Space ◽  
Hamiltonian Constraint ◽  
Area Operator ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum

In this paper canonical quantum gravity on noncommutative space–time is considered. The corresponding generalized classical theory is formulated by using the Moyal star product, which enables the representation of the field quantities depending on noncommuting coordinates by generalized quantities depending on usual coordinates. But not only the classical theory has to be generalized in analogy to other field theories. Besides, the necessity arises to replace the commutator between the gravitational field operator and its canonical conjugated quantity by a corresponding generalized expression on noncommutative space–time. Accordingly the transition to the quantum theory has also to be performed in a generalized way and leads to extended representations of the quantum theoretical operators. If the generalized representations of the operators are inserted to the generalized constraints, one obtains the corresponding generalized quantum constraints including the Hamiltonian constraint as dynamical constraint. After considering quantum geometrodynamics under incorporation of a coupling to matter fields, the theory is transferred to the Ashtekar formalism. The holonomy representation of the gravitational field as it is used in loop quantum gravity opens the possibility to calculate the corresponding generalized area operator.

scholarly journals MINISUPERSPACE MODEL FOR REVISED CANONICAL QUANTUM GRAVITY

2004 ◽  
Vol 13 (08) ◽  
pp. 1703-1718 ◽  
Author(s):  
GIOVANNI MONTANI
Keyword(s):  
Quantum Gravity ◽  
Reference Frame ◽  
Quantum Dynamics ◽  
Cosmological Solution ◽  
Canonical Quantization ◽  
Hamiltonian Operator ◽  
Big Bang ◽  
Dust Fluid ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum

We present a reformulation of the canonical quantization of gravity, as referred to the minisuperspace; the new approach is based on fixing a Gaussian (or synchronous) reference frame and then quantizing the system via the reconstruction of a suitable constraint; then the quantum dynamics is re-stated in a generic coordinates system and it becomes dependent on the lapse function. The analysis follows a parallelism with the case of the non-relativistic particle and leads to the minisuperspace implementation of the so-called kinematical action as proposed in Ref. 1 (here almost coinciding also with the approach presented in Ref. 2). The new constraint leads to a Schrödinger equation for the system, i.e. to non-vanishing eigenvalues for the super-Hamiltonian operator; the physical interpretation of this feature relies on the appearance of a "dust fluid" (non-positive definite) energy density, i.e. a kind of "materialization" of the reference frame. As an example of minisuperspace model, we consider a Bianchi type IX Universe, for which some dynamical implications of the revised canonical quantum gravity are discussed. We also show how, on the classical limit, the presence of the dust fluid can have relevant cosmological issues. Finally we upgrade our analysis by its extension to the generic cosmological solution, which is performed in the so-called long-wavelength approximation. In fact, near the Big-Bang, we can neglect the spatial gradients of the dynamical variables and proceed to implement, in each space point, the same minisuperspace paradigm valid for the Bianchi IX model.

scholarly journals Black-hole horizons in modified spacetime structures arising from canonical quantum gravity

2011 ◽  
Vol 28 (18) ◽  
pp. 185006 ◽  
Author(s):  
Martin Bojowald ◽  
George M Paily ◽  
Juan D Reyes ◽  
Rakesh Tibrewala
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum

scholarly journals HERACLITEAN TIME PROPOSAL REVISITED

1995 ◽  
Vol 04 (01) ◽  
pp. 97-103 ◽  
Author(s):  
ORFEU BERTOLAMI
Keyword(s):  
General Relativity ◽  
Wave Function ◽  
Quantum Gravity ◽  
Relaxation Mechanism ◽  
Cosmological Term ◽  
Classical Level ◽  
Canonical Quantum Gravity ◽  
The Universe ◽  
Canonical Quantum

Difficulties in the interpretation of the wave function of the Universe in canonical quantum gravity suggest that the use of dynamical variables to play the role of time is not quite consistent. A formulation of canonical quantum gravity in which time is an extrinsic variable has been previously studied with the problem of being compatible, at the classical level, with General Relativity with a nonvanishing unspecified cosmological constant. We argue that this last problem can be circumvented by introducing a nondynamical scalar field which allows for a relaxation mechanism for the cosmological term.

Forming the Canon

2020 ◽  
pp. 160-192
Author(s):  
Dean Rickles
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Quantum Gravity ◽  
Early Development ◽  
Subsequent Development ◽  
Hamiltonian Form ◽  
Coordinate Transformations ◽  
Canonical Approach ◽  
Canonical Quantum Gravity ◽  
Canonical Quantum

This chapter charts the early development of the canonical quantum gravity (that is, the quantization of the gravitational field in Hamiltonian form). What we find in this period include: the establishment of a procedure for quantizing in curved spaces; the first expressions for the Hamiltonian of general relativity; recognition of the existence and importance of constraints (i.e. the generators of infinitesimal coordinate transformations); a focus on the problem of observables (and the realisation of conceptual implications in defining these for generally relativistic theories), and a (template of a) method for quantizing the theory. Although it commenced relatively early, the canonical approach was slow in its subsequent development. This had two sources: (1) it required the introduction of tools and concepts from outside of quantum gravity proper (namely, the constraint machinery and the parameter formalism); (2) by its very nature, it is highly rigorous in a conceptual sense, demanding lots of groundwork to be established, in terms of the structure of physical observables, before the actual issue of quantization can even be considered. Work was further complicated by the fact that these two sources of difficulty happened to be entangled. Particular emphasis is placed on the parameter formalism of Paul Weiss.

scholarly journals COSMOLOGICAL ISSUES FOR REVISED CANONICAL QUANTUM GRAVITY

2003 ◽  
Vol 12 (08) ◽  
pp. 1445-1458 ◽  
Author(s):  
GIOVANNI MONTANI
Keyword(s):  
Quantum Gravity ◽  
Canonical Quantization ◽  
Cosmological Problem ◽  
Self Consistent ◽  
Dust Fluid ◽  
Canonical Quantum Gravity ◽  
External Time ◽  
Matter Component ◽  
Canonical Quantum

In a recent work1 we presented a reformulation of the canonical quantum gravity, based on adding the so-called kinematical term to the gravity-matter action. This revised approach leads to a self-consistent canonical quantization of the 3-geometries, which referred to the external time as provided via the added term. Here, we show how the kinematical term can be interpreted in terms of a non-relativistic dust fluid which plies the role of a "real clock" for the quantum gravity theory, and, in the WKB limit of a cosmological problem, makes account for a dark matter component which, at present time, could play a dynamical role.

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