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):  
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

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):  
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 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 Remarks on Remnants by Fermions’ Tunnelling from Black Strings

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Deyou Chen ◽  
Zhonghua Li
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Final Stage ◽  
Generalized Uncertainty Principle ◽  
Black Hole Evaporation ◽  
Quantum Numbers ◽  
Black Strings

Hawking’s calculation is unable to predict the final stage of the black hole evaporation. When effects of quantum gravity are taken into account, there is a minimal observable length. In this paper, we investigate fermions’ tunnelling from the charged and rotating black strings. With the influence of the generalized uncertainty principle, the Hawking temperatures are not only determined by the rings, but also affected by the quantum numbers of the emitted fermions. Quantum gravity corrections slow down the increases of the temperatures, which naturally leads to remnants left in the evaporation.

scholarly journals Rainbow Gravity Corrections to the Entropic Force

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong-Wen Feng ◽  
Shu-Zheng Yang
Keyword(s):  
Black Hole ◽  
Field Equation ◽  
Quantum Gravity ◽  
Gravity Model ◽  
Einstein Field Equation ◽  
Friedmann Equation ◽  
Quantum Corrections ◽  
Entropic Force ◽  
Planck Length ◽  
Multifunctional Properties

The entropic force attracts a lot of interest for its multifunctional properties. For instance, Einstein’s field equation, Newton’s law of gravitation, and the Friedmann equation can be derived from the entropic force. In this paper, utilizing a new kind of rainbow gravity model that was proposed by Magueijo and Smolin, we explore the quantum gravity corrections to the entropic force. First, we derive the modified thermodynamics of a rainbow black hole via its surface gravity. Then, according to Verlinde’s theory, the quantum corrections to the entropic force are obtained. The result shows that the modified entropic force is related not only to the properties of the black hole but also to the Planck length lp and the rainbow parameter γ. Furthermore, based on the rainbow gravity corrected entropic force, the modified Einstein field equation and the modified Friedmann equation are also derived.

SPACE–TIME ENERGY–MOMENTUM, THE OBSERVER AND UNCERTAINTY IN GENERAL RELATIVITY

2010 ◽  
Vol 19 (14) ◽  
pp. 2353-2359 ◽  
Author(s):  
F. I. COOPERSTOCK ◽  
M. J. DUPRE
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Uncertainty Principle ◽  
Ricci Tensor ◽  
Space Time ◽  
Energy Integral ◽  
New Approach ◽  
Extended Space ◽  
Energy And Momentum

In this essay, we introduce a new approach to energy–momentum in general relativity. Space–time, as opposed to space, is recognized as the necessary arena for its examination, leading us to define new extended space–time energy and momentum constructs. From local and global considerations, we conclude that the Ricci tensor is the required element for a localized expression of energy–momentum to include the gravitational field. We present and rationalize a fully invariant extended expression for space–time energy, guided by Tolman's well-known energy integral for an arbitrary bounded stationary system. This raises fundamental issues which we discuss. The role of the observer emerges naturally and we are led to an extension of the uncertainty principle to general relativity, of particular relevance to ultra-strong gravity.

scholarly journals Prospects for probing strong gravity with a pulsar-black hole system

2012 ◽  
Vol 8 (S291) ◽  
pp. 171-176 ◽  
Author(s):  
N. Wex ◽  
K. Liu ◽  
R. P. Eatough ◽  
M. Kramer ◽  
J. M. Cordes ◽  
...  
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Quadrupole Moment ◽  
Strong Field ◽  
Mass Measurement ◽  
Test System ◽  
Space Time ◽  
High Grade ◽  
Radio Telescopes ◽  
Strong Gravity

AbstractThe discovery of a pulsar (PSR) in orbit around a black hole (BH) is expected to provide a superb new probe of relativistic gravity and BH properties. Apart from a precise mass measurement for the BH, one could expect a clean verification of the dragging of space-time caused by the BH spin. In order to measure the quadrupole moment of the BH for testing the no-hair theorem of general relativity (GR), one has to hope for a sufficiently massive BH. In this respect, a PSR orbiting the super-massive BH in the center of our Galaxy would be the ultimate laboratory for gravity tests with PSRs. But even for gravity theories that predict the same properties for BHs as GR, a PSR-BH system would constitute an excellent test system, due to the high grade of asymmetry in the strong field properties of these two components. Here we highlight some of the potential gravity tests that one could expect from different PSR-BH systems, utilizing present and future radio telescopes, like FAST and SKA.

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