scholarly journals Renormalizing spacetime

2018 ◽  
Vol 27 (16) ◽  
pp. 1950008 ◽  
Author(s):  
D. N. Coumbe
Keyword(s):  
Quantum Gravity ◽  
Functional Form ◽  
Distance Scale ◽  
Metric Tensor ◽  
Weyl Transformation ◽  
Renormalization Factor ◽  
Consistent Field ◽  
Energy And Momentum ◽  
Proper Length ◽  
Field Renormalization

We propose that the consistent field renormalization of gravity requires a specific Weyl transformation of the metric tensor. As a consequence, proper length and time, as well as energy and momentum, become functions of scale. We estimate the functional form of the field renormalization factor by imposing a minimum resolvable distance scale under an infinitesimal Weyl transformation. The derived transformation is applied to two key problems in quantum gravity: its nonconformal scaling and nonrenormalizability.

scholarly journals Global properties of physically interesting Lorentzian spacetimes

2016 ◽  
Vol 25 (14) ◽  
pp. 1650106
Author(s):  
Deloshan Nawarajan ◽  
Matt Visser
Keyword(s):  
Standard Model ◽  
Quantum Gravity ◽  
Particle Physics ◽  
Causal Structure ◽  
Complex Structure ◽  
Good Representation ◽  
Global Features ◽  
Metric Tensor ◽  
Global Issues ◽  
The Standard Model

Under normal circumstances most members of the general relativity community focus almost exclusively on the local properties of spacetime, such as the locally Euclidean structure of the manifold and the Lorentzian signature of the metric tensor. When combined with the classical Einstein field equations this gives an extremely successful empirical model of classical gravity and classical matter — at least as long as one does not ask too many awkward questions about global issues, (such as global topology and global causal structure). We feel however that this is a tactical error — even without invoking full-fledged “quantum gravity” we know that the standard model of particle physics is also an extremely good representation of some parts of empirical reality; and we had better be able to carry over all the good features of the standard model of particle physics — at least into the realm of semi-classical quantum gravity. Doing so gives us some interesting global features that spacetime should possess: On physical grounds spacetime should be space-orientable, time-orientable, and spacetime-orientable, and it should possess a globally defined tetrad (vierbein, or in general a globally defined vielbein/[Formula: see text]-bein). So on physical grounds spacetime should be parallelizable. This strongly suggests that the metric is not the fundamental physical quantity; a very good case can be made for the tetrad being more fundamental than the metric. Furthermore, a globally-defined “almost complex structure” is almost unavoidable. Ideas along these lines have previously been mooted, but much is buried in the pre- arXiv literature and is either forgotten or inaccessible. We shall revisit these ideas taking a perspective very much based on empirical physical observation.

TWO-LOOP APPROACH TO THE EFFECTIVE ACTION IN QUANTUM GRAVITY

1992 ◽  
Vol 07 (14) ◽  
pp. 3203-3233 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
S. D. ODINTSOV ◽  
O. A. FONAREV
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Minkowski Space ◽  
Effective Action ◽  
Dimensional Regularization ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
Metric Tensor ◽  
First Time

For the first time we present the general formalism and results of calculation of the two-loop effective action in Einstein quantum gravity on the background MN × Tk, where MN is Minkowski space and Tk is a k-dimensional torus. We discuss the case of a zero cosmological constant as well as of a nonzero one. The method of calculating variations of the action on a metric tensor and the technique of calculating momentum integrals in dimensional regularization are presented. Some applications to spontaneous compactification are discussed, as well as some prospects.

scholarly journals Outline for a Quantum Theory of Gravity

2019 ◽  
Vol 74 (5) ◽  
pp. 383-386
Author(s):  
Tejinder P. Singh
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Experimental Tests ◽  
World Sheet ◽  
Action Function ◽  
Relativistic Limit ◽  
Metric Tensor ◽  
Theory Of Gravity ◽  
Matrix Dynamics

AbstractBy invoking an asymmetric metric tensor, and borrowing ideas from non-commutative geometry, string theory, and trace dynamics, we propose an action function for quantum gravity. The action is proportional to the four-dimensional non-commutative curvature scalar (which is torsion dependent), which is sourced by the Nambu–Goto world-sheet action for a string plus the Kalb–Ramond string action. This ‘quantum gravity’ is actually a non-commutative classical matrix dynamics, and the only two fundamental constants in the theory are the square of the Planck length and the speed of light. By treating the entity described by this action as a microstate, one constructs the statistical thermodynamics of a large number of such microstates, in the spirit of trace dynamics. Quantum field theory (and ℏ) and quantum general relativity (and G) emerge from the underlying matrix dynamics in the thermodynamic limit. Statistical fluctuations, which are inevitably present about equilibrium, are the source for spontaneous localisation, which drives macroscopic quantum gravitational systems to the classical general relativistic limit. While the mathematical formalism governing these ideas remains to be developed, we hope to highlight here the deep connection between quantum foundations and the sought-for quantum theory of gravity. In the sense described in this article, ongoing experimental tests of spontaneous collapse theories are in fact also tests of string theory!

scholarly journals Space-Time Second-Quantization Effects and the Quantum Origin of Cosmological Constant in Covariant Quantum Gravity

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 287 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Gravitational Field ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Proper Time ◽  
Theoretical Background ◽  
Space Time ◽  
Einstein Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Covariant Quantum

Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant proper-time parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend generally also on the realization of the quantum probability density for the quantum gravitational field tensor. The emerging physical picture predicts a generally non-stationary quantum cosmological constant which originates from fluctuations (i.e., gradients) of vacuum quantum gravitational energy density and is consistent with the existence of quantum massive gravitons.

scholarly journals The Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 370
Author(s):  
Massimo Tessarotto ◽  
Claudio Cremaschini
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Form Factor ◽  
Quantum Gravity ◽  
Metric Tensor ◽  
Covariant Approach ◽  
Covariant Quantum ◽  
Background Space ◽  
Hamilton Equations ◽  
Black Hole Solutions

An excruciating issue that arises in mathematical, theoretical and astro-physics concerns the possibility of regularizing classical singular black hole solutions of general relativity by means of quantum theory. The problem is posed here in the context of a manifestly covariant approach to quantum gravity. Provided a non-vanishing quantum cosmological constant is present, here it is proved how a regular background space-time metric tensor can be obtained starting from a singular one. This is obtained by constructing suitable scale-transformed and conformal solutions for the metric tensor in which the conformal scale form factor is determined uniquely by the quantum Hamilton equations underlying the quantum gravitational field dynamics.

scholarly journals ON THE MOTION OF A TEST PARTICLE AROUND A GLOBAL MONOPOLE IN A MODIFIED GRAVITY

2012 ◽  
Vol 27 (30) ◽  
pp. 1250177 ◽  
Author(s):  
T. R. P. CARAMÊS ◽  
E. R. BEZERRA DE MELLO ◽  
M. E. X. GUIMARÃES
Keyword(s):  
Test Particle ◽  
Modified Gravity ◽  
Functional Form ◽  
Weak Field ◽  
Radial Coordinate ◽  
Spherically Symmetric ◽  
Global Monopole ◽  
Field Equations ◽  
Metric Tensor ◽  
Spherically Symmetric Metric

In this paper we suggest an approach to analyze the motion of a test particle in the spacetime of a global monopole within a f(R)-like modified gravity. The field equations are written in a simplified form in terms of [Formula: see text]. Since we are dealing with a spherically symmetric metric, we express F(R) as a function of the radial coordinate only, e.g., [Formula: see text]. So, the choice of a specific form for f(R) will be equivalent to adopt an Ansatz for [Formula: see text] . By choosing an explicit functional form for [Formula: see text], we obtain the weak field solutions for the metric tensor also compute the time-like geodesics and analyze the motion of a massive test particle. An interesting feature is an emerging attractive force exerted by the monopole on the particle.

scholarly journals Quantum gravity without vacuum dispersion

2017 ◽  
Vol 26 (10) ◽  
pp. 1750119 ◽  
Author(s):  
D. N. Coumbe
Keyword(s):  
Quantum Gravity ◽  
Quantum Correction ◽  
Functional Form ◽  
Geodesic Distance ◽  
Generalized Uncertainty Principle ◽  
Scale Transformation ◽  
Area Spectrum ◽  
Time Interval ◽  
Speed Of Light ◽  
Dynamical Triangulation

A generic prediction of quantum gravity is the vacuum dispersion of light, and hence that a photon’s speed depends on its energy. We present further numerical evidence for a scale-dependent speed of light in the causal dynamical triangulation (CDT) approach to quantum gravity. We show that the observed scale-dependent speed of light in CDT can be accounted for by a scale-dependent transformation of geodesic distance, whose specific functional form implies a discrete equidistant area spectrum. We make two nontrivial tests of the proposed scale transformation: a comparison with the leading-order quantum correction to the gravitational potential and a comparison with the generalized uncertainty principle. In both cases, we obtain the same functional form. However, contrary to the widespread prediction of vacuum dispersion in quantum gravity, numerous experiments have now definitively ruled out linear vacuum dispersion beyond Planckian energy scales [Formula: see text], and have even constrained quadratic dispersion at the level [Formula: see text]. Motivated by these experimental constraints, we seek to reconcile quantum gravity with the absence of vacuum dispersion. We point out that given a scale-dependent geodesic distance, a scale-dependent time interval becomes essential to maintaining an invariant speed of light. We show how a particular scale-dependent time interval allows a photon’s speed to remain independent of its energy.

scholarly journals Quantum-Gravity Stochastic Effects on the de Sitter Event Horizon

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 696 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Quantum Gravity ◽  
Event Horizon ◽  
Analytical Calculation ◽  
Tunneling Effect ◽  
Covariant Theory ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Stochastic Effects

The stochastic character of the cosmological constant arising from the non-linear quantum-vacuum Bohm interaction in the framework of the manifestly-covariant theory of quantum gravity (CQG theory) is pointed out. This feature is shown to be consistent with the axiomatic formulation of quantum gravity based on the hydrodynamic representation of the same CQG theory developed recently. The conclusion follows by investigating the indeterminacy properties of the probability density function and its representation associated with the quantum gravity state, which corresponds to a hydrodynamic continuity equation that satisfies the unitarity principle. As a result, the corresponding form of stochastic quantum-modified Einstein field equations is obtained and shown to admit a stochastic cosmological de Sitter solution for the space-time metric tensor. The analytical calculation of the stochastic averages of relevant physical observables is obtained. These include in particular the radius of the de Sitter sphere fixing the location of the event horizon and the expression of the Hawking temperature associated with the related particle tunneling effect. Theoretical implications for cosmology and field theories are pointed out.

scholarly journals Quantum-Gravity Screening Effect of the Cosmological Constant in the DeSitter Space–Time

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 531 ◽  
Author(s):  
Claudio Cremaschini ◽  
Massimo Tessarotto
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Space Time ◽  
Energy Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Metric Tensor ◽  
Screening Effect ◽  
Periodic Perturbations ◽  
Desitter Space

Small-amplitude quantum-gravity periodic perturbations of the metric tensor, occurring in sequences of phase-shifted oscillations, are investigated for vacuum conditions and in the context of the manifestly-covariant theory of quantum gravity. The theoretical background is provided by the Hamiltonian representation of the quantum hydrodynamic equations yielding, in turn, quantum modifications of the Einstein field equations. It is shown that in the case of the DeSitter space–time sequences of small-size periodic perturbations with prescribed frequency are actually permitted, each one with its characteristic initial phase. The same perturbations give rise to non-linear modifications of the Einstein field equations in terms of a suitable stochastic-averaged and divergence-free quantum stress-energy tensor. As a result, a quantum-driven screening effect arises which is shown to affect the magnitude of the cosmological constant. Observable features on the DeSitter space–time solution and on the graviton mass estimate are pointed out.

Voyager UVS observations of stellar occultations by the rings of Saturn

1984 ◽  
Vol 75 ◽  
pp. 265-277
Author(s):  
J.B. Holbelg ◽  
W.T. Forrester
Keyword(s):  
Optical Depth ◽  
Distance Scale ◽  
Density Waves ◽  
Ring Density ◽  
Stellar Occultations ◽  
Saturn’S Rings ◽  
Saturn's Rings

ABSTRACTDuring the Voyager 1 and 2 Saturn encounters the ultraviolet spectrometers observed three separate stellar occultations by Saturn's rings. Together these three observations, which sampled the optical depth of the rings at resolutions from 3 to 6 km. can be used to establish a highly accurate distance scale allowing the identification of numerous ring features associated with resonances due to exterior satellites. Three separate observations of an eccentric ringlet near the location of the Titan apsidal resonance are discussed along with other ringlet-resonance associations occurring in the C ring. Density waves occurring in the A and B rings are reviewed and a detailed discussion of the analysis of one of these features is presented.

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