scholarly journals Covariant Space-Time Line Elements in the Friedmann-Lemaitre-Robertson-Walker Geometry

2021 ◽  
Author(s):  
David Escors ◽  
Grazyna Kochan
Keyword(s):  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Lorentz Invariance ◽  
Space Time ◽  
Planck Length ◽  
Time Line ◽  
Geometric Uncertainty ◽  
Expected Length ◽  
Gravity Theories ◽  
Line Elements

Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.

scholarly journals Covariant Space-Time Line Elements in the Friedmann-Lemaitre-Robertson-Walker Geometry

2021 ◽  
Author(s):  
David Escors ◽  
Grazyna Kochan
Keyword(s):  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Lorentz Invariance ◽  
Space Time ◽  
Planck Length ◽  
Time Line ◽  
Geometric Uncertainty ◽  
Expected Length ◽  
Gravity Theories ◽  
Line Elements

Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.

scholarly journals Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

Physics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 790-798
Author(s):  
David Escors ◽  
Grazyna Kochan
Keyword(s):  
General Relativity ◽  
Uncertainty Principle ◽  
Geodesic Equation ◽  
Space Time ◽  
Minimum Length ◽  
Exclusion Zone ◽  
Minkowski Metric ◽  
Time Line ◽  
Geometric Uncertainty ◽  
Classical Gravity

The classical uncertainty principle inequalities are imposed over the general relativity geodesic equation as a mathematical constraint. In this way, the uncertainty principle is reformulated in terms of proper space–time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirms the need for a minimum length of space–time line element in the geodesic, which depends on a Lorentz-covariant geodesic-derived scalar. In agreement with quantum gravity theories, GeUP imposes a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone is found around the singularity where uncertainty in space-time diverged to infinity.

scholarly journals Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

2021 ◽  
Author(s):  
David Escors ◽  
Grazyna Kochan
Keyword(s):  
Mathematical Model ◽  
General Relativity ◽  
Black Hole ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Zero Point ◽  
Space Time ◽  
Planck Length ◽  
Exclusion Zone ◽  
Curvature Perturbation

General relativity is a theory for gravitation based on Riemannian geometry, difficult to compatibilize with quantum mechanics. This is evident in relativistic problems in which quantum effects cannot be discarded. For example in quantum gravity, gravitation of zero-point energy or events close to a black hole singularity. Here, we set up a mathematical model to select general relativity geodesics according to compatibility with the uncertainty principle. To achieve this, we derived a geometric expression of the uncertainty principle (GeUP). This formulation identified proper space-time length with Planck length by a geodesic-derived scalar. GeUP imposed a minimum allowed value for the interval of proper space-time which depended on the particular space-time geometry. GeUP forced the introduction of a “zero-point” curvature perturbation over flat Minkowski space, caused exclusively by quantum uncertainty but not to gravitation. When applied to the Schwarzschild metric and choosing radial-dependent geodesics, our mathematical model identified a particle exclusion zone close to the singularity, similar to calculations by loop quantum gravity. For a 2 black hole merger, this exclusion zone was shown to have a radius that cannot go below a value proportional to the energy/mass of the incoming black hole multiplied by Planck length.

scholarly journals Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

2021 ◽  
Author(s):  
David Escors ◽  
Grazyna Kochan
Keyword(s):  
Mathematical Model ◽  
General Relativity ◽  
Black Hole ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Zero Point ◽  
Space Time ◽  
Planck Length ◽  
Exclusion Zone ◽  
Curvature Perturbation

General relativity is a theory for gravitation based on Riemannian geometry, difficult to compatibilize with quantum mechanics. This is evident in relativistic problems in which quantum effects cannot be discarded. For example in quantum gravity, gravitation of zero-point energy or events close to a black hole singularity. Here, we set up a mathematical model to select general relativity geodesics according to compatibility with the uncertainty principle. To achieve this, we derived a geometric expression of the uncertainty principle (GUP). This formulation identified proper space-time length with Planck length by a geodesic-derived scalar. GUP imposed a minimum allowed value for the interval of proper space-time which depended on the particular space-time geometry. GUP forced the introduction of a “zero-point” curvature perturbation over flat Minkowski space, caused exclusively by quantum uncertainty but not to gravitation. When applied to the Schwarzschild metric and choosing radial-dependent geodesics, our mathematical model identified a particle exclusion zone close to the singularity, similar to calculations by loop quantum gravity. For a 2 black hole merger, this exclusion zone was shown to have a radius that cannot go below a value proportional to the energy/mass of the incoming black hole multiplied by Planck length.

scholarly journals Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

2021 ◽  
Author(s):  
David Escors ◽  
Grazyna Kochan
Keyword(s):  
General Relativity ◽  
Uncertainty Principle ◽  
Geodesic Equation ◽  
Space Time ◽  
Minimum Length ◽  
Exclusion Zone ◽  
Minkowski Metric ◽  
Time Line ◽  
Geometric Uncertainty ◽  
Classical Gravity

The classical uncertainty principle inequalities were imposed as a mathematical constraint over the general relativity geodesic equation. In this way, the uncertainty principle was reformulated in terms of the proper space-time length element, Planck length and a geodesic-derived scalar, leading to a geometric expression for the uncertainty principle (GeUP). This re-formulation confirmed the necessity for a minimum length for the space-time line element in the geodesic, dependent on a geodesic-derived scalar which made the expression Lorentz-covariant. In agreement with quantum gravity theories, GeUP required the imposition of a perturbation over the background Minkowski metric unrelated to classical gravity. When applied to the Schwarzschild metric, a geodesic exclusion zone was found around the singularity where uncertainty in space-time diverged to infinity.

scholarly journals A quantized spacetime based on Spin(3,1) symmetry

2016 ◽  
Vol 25 (13) ◽  
pp. 1645004
Author(s):  
Pisin Chen ◽  
Hsu-Wen Chiang ◽  
Yao-Chieh Hu
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Generalized Uncertainty Principle ◽  
Spin Network ◽  
Fundamental Symmetry ◽  
New Type ◽  
Gravity Theories

We introduce a new type of the spacetime quantization based on the spinorial description suggested by loop quantum gravity. Specifically, we build our theory on a string theory inspired [Formula: see text] worldsheet action. Because of its connection with quantum gravity theories, our proposal may in principle link back to string theory, connect to loop quantum gravity where SU(2) is suggested as the fundamental symmetry, or serve as a Lorentzian spin network. We derive the generalized uncertainty principle and demonstrate the holographic nature of our theory. Due to the quantization of spacetime, geodesics in our theory are fuzzy, but the fuzziness is shown to be much below conceivable astrophysical bounds.

scholarly journals Black-Hole Models in Loop Quantum Gravity

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 125
Author(s):  
Martin Bojowald
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Space Time ◽  
Classical Solutions ◽  
General Covariance ◽  
White Hole ◽  
Signature Change ◽  
Generalized Covariance ◽  
Line Elements

Dynamical black-hole scenarios have been developed in loop quantum gravity in various ways, combining results from mini and midisuperspace models. In the past, the underlying geometry of space-time has often been expressed in terms of line elements with metric components that differ from the classical solutions of general relativity, motivated by modified equations of motion and constraints. However, recent results have shown by explicit calculations that most of these constructions violate general covariance and slicing independence. The proposed line elements and black-hole models are therefore ruled out. The only known possibility to escape this sentence is to derive not only modified metric components but also a new space-time structure which is covariant in a generalized sense. Formally, such a derivation is made available by an analysis of the constraints of canonical gravity, which generate deformations of hypersurfaces in space-time, or generalized versions if the constraints are consistently modified. A generic consequence of consistent modifications in effective theories suggested by loop quantum gravity is signature change at high density. Signature change is an important ingredient in long-term models of black holes that aim to determine what might happen after a black hole has evaporated. Because this effect changes the causal structure of space-time, it has crucial implications for black-hole models that have been missed in several older constructions, for instance in models based on bouncing black-hole interiors. Such models are ruled out by signature change even if their underlying space-times are made consistent using generalized covariance. The causal nature of signature change brings in a new internal consistency condition, given by the requirement of deterministic behavior at low curvature. Even a causally disconnected interior transition, opening back up into the former exterior as some kind of astrophysical white hole, is then ruled out. New versions consistent with both generalized covariance and low-curvature determinism are introduced here, showing a remarkable similarity with models developed in other approaches, such as the final-state proposal or the no-transition principle obtained from the gauge-gravity correspondence.

scholarly journals GRAVITY IN QUANTUM SPACE–TIME

2010 ◽  
Vol 19 (14) ◽  
pp. 2385-2392 ◽  
Author(s):  
GIOVANNI AMELINO-CAMELIA ◽  
NICCOLÒ LORET ◽  
GIANLUCA MANDANICI ◽  
FLAVIO MERCATI
Keyword(s):  
Quantum Gravity ◽  
Gravitational Collapse ◽  
Particle Physics ◽  
Space Time ◽  
Valuable Insight ◽  
Quantum Space ◽  
Particle Propagation ◽  
Gravity Theories

The literature on quantum-gravity-inspired scenarios for the quantization of space–time has so far focused on particle-physics-like studies. This is partly justified by the present limitations of our understanding of quantum gravity theories, but we here argue that valuable insight can be gained through semi-heuristic analyses of the implications for gravitational phenomena of some results obtained in the quantum space–time literature. In particular, we show that the types of description of particle propagation that emerged in certain quantum space–time frameworks have striking implications for gravitational collapse and for the behavior of gravity at large distances.

scholarly journals The quantum echo of the early universe

2015 ◽  
Vol 93 (9) ◽  
pp. 968-970 ◽  
Author(s):  
Ana Blasco ◽  
Luis J. Garay ◽  
Mercedes Martín-Benito ◽  
Eduardo Martín-Martínez
Keyword(s):  
Quantum Gravity ◽  
Early Universe ◽  
Space Time ◽  
Quantum Fields ◽  
Gravitational Effects ◽  
History Of ◽  
Gravity Theories

We show that the fluctuations of quantum fields as seen by late comoving observers are significantly influenced by the history of the early Universe, and therefore they transmit information about the nature of space–time in timescales when quantum gravitational effects were non-negligible. We discuss how this may be observable even nowadays and thus used to build falsifiability tests of quantum gravity theories.

scholarly journals POSSIBLE ASTROPHYSICAL PROBES OF QUANTUM GRAVITY

2002 ◽  
Vol 17 (15n17) ◽  
pp. 1025-1035 ◽  
Author(s):  
SUBIR SARKAR
Keyword(s):  
Quantum Gravity ◽  
Active Galactic Nuclei ◽  
Gamma Ray ◽  
Lorentz Invariance ◽  
Galactic Nuclei ◽  
High Energy ◽  
Space Time ◽  
Classical Perception ◽  
Relativistic Particles ◽  
Satisfactory Theory

A satisfactory theory of quantum gravity will very likely require modification of our classical perception of space-time, perhaps by giving it a 'foamy' structure at scales of order the Planck length. This is expected to modify the propagation of photons and other relativistic particles such as neutrinos, such that they will experience a non-trivial refractive index even in vacuo. The implied spontaneous violation of Lorentz invariance may also result in alterations of kinematical thresholds for key astrophysical processes involving high energy cosmic radiation. We discuss experimental probes of these possible manifestations of the fundamental quantum nature of space-time using observations of distant astrophysical sources such as gamma-ray bursts and active galactic nuclei.

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