Curved Space and General Relativity

1986 ◽  
Keyword(s):  
General Relativity ◽  
Curved Space

GRAVITY CAN BE OBSERVED IN THE ABSENCE OF CURVED SPACETIME, THUS CURVED SPACETIME IS NOT RESPONCIBLE FOR GRAVITY

2015 ◽  
Vol 8 (1) ◽  
pp. 1976-1981
Author(s):  
Casey McMahon
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Relative Position ◽  
Gravitational Force ◽  
Curved Spacetime ◽  
Relative Time ◽  
Curved Space ◽  
Spacetime Curvature ◽  
Equivalence Model ◽  
The Universe

The principle postulate of general relativity appears to be that curved space or curved spacetime is gravitational, in that mass curves the spacetime around it, and that this curved spacetime acts on mass in a manner we call gravity. Here, I use the theory of special relativity to show that curved spacetime can be non-gravitational, by showing that curve-linear space or curved spacetime can be observed without exerting a gravitational force on mass to induce motion- as well as showing gravity can be observed without spacetime curvature. This is done using the principles of special relativity in accordance with Einstein to satisfy the reader, using a gravitational equivalence model. Curved spacetime may appear to affect the apparent relative position and dimensions of a mass, as well as the relative time experienced by a mass, but it does not exert gravitational force (gravity) on mass. Thus, this paper explains why there appears to be more gravity in the universe than mass to account for it, because gravity is not the resultant of the curvature of spacetime on mass, thus the “dark matter” and “dark energy” we are looking for to explain this excess gravity doesn’t exist.

scholarly journals Theory of Nonlocal Point Transformations in General Relativity

2016 ◽  
Vol 2016 ◽  
pp. 1-32 ◽  
Author(s):  
Massimo Tessarotto ◽  
Claudio Cremaschini
Keyword(s):  
General Relativity ◽  
Field Equations ◽  
Traditional Concept ◽  
Curved Space ◽  
Point Transformations ◽  
Functional Setting ◽  
Mathematical Foundations ◽  
The Relationship ◽  
Metric Tensors

A discussion of the functional setting customarily adopted in General Relativity (GR) is proposed. This is based on the introduction of the notion of nonlocal point transformations (NLPTs). While allowing the extension of the traditional concept of GR-reference frame, NLPTs are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems. For this purpose in the paper the mathematical foundations of NLPT-theory are laid down and basic physical implications are considered. In particular, explicit applications of the theory are proposed, which concern(1)a solution to the so-called Einstein teleparallel problem in the framework of NLPT-theory;(2)the determination of the tensor transformation laws holding for the acceleration 4-tensor with respect to the group of NLPTs and the identification of NLPT-acceleration effects, namely, the relationship established via general NLPT between particle 4-acceleration tensors existing in different curved space-times;(3)the construction of the nonlocal transformation law connecting different diagonal metric tensors solution to the Einstein field equations; and(4)the diagonalization of nondiagonal metric tensors.

Zum Übergang von der Wellenoptik zur geometrischen Optik in der allgemeinen Relativitätstheorie

1967 ◽  
Vol 22 (9) ◽  
pp. 1328-1332 ◽  
Author(s):  
Jürgen Ehlers
Keyword(s):  
General Relativity ◽  
Maxwell Equations ◽  
Expansion Method ◽  
Flat Space ◽  
Space Time ◽  
Moving Medium ◽  
Formal Similarity ◽  
Curved Space ◽  
Optical Metric ◽  
Series Expansion Method

The transition from the (covariantly generalized) MAXWELL equations to the geometrical optics limit is discussed in the context of general relativity, by adapting the classical series expansion method to the case of curved space time. An arbitrarily moving ideal medium is also taken into account, and a close formal similarity between wave propagation in a moving medium in flat space time and in an empty, gravitationally curved space-time is established by means of a normal hyperbolic optical metric.

VAN DER WAALS FORCES IN CURVED SPACE AS A QUANTUM TOOL TO TEST GENERAL RELATIVITY THEORY

2005 ◽  
Vol 14 (06) ◽  
pp. 995-1008 ◽  
Author(s):  
FABRIZIO PINTO
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Experimental Test ◽  
Point Charge ◽  
Van Der Waals ◽  
Atom Interferometry ◽  
Relativity Theory ◽  
Spherically Symmetric ◽  
General Relativity Theory ◽  
Curved Space

It has been known shortly after the introduction of the general relativity theory that the electrostatic Coulomb potential of a point charge supported in a gravitational field is not spherically symmetric and becomes warped in curved space. Under ordinary laboratory conditions, this effect is quite small and has never been directly observed. Surprisingly, this distortion causes the appearance of a hitherto unknown, topologically complex non-central van der Waals force whose detection is well within range of existing trapped atom interferometry techniques. This will allow for an unexpected experimental test of gravity theory by means of quantum-electro-dynamical interatomic forces.

scholarly journals Four interactions in the sedenion curved spaces

2019 ◽  
Vol 16 (02) ◽  
pp. 1950019 ◽  
Author(s):  
Zi-Hua Weng
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Classical Mechanics ◽  
Flat Space ◽  
Field Equations ◽  
Curved Space ◽  
Gravitational Fields ◽  
Curved Spaces ◽  
Spatial Parameters ◽  
Physical Quantities

The paper aims to apply the complex-sedenions to explore the field equations of four fundamental interactions, which are relevant to the classical mechanics and quantum mechanics, in the curved spaces. Maxwell was the first to utilize the quaternions to describe the property of electromagnetic fields. Nowadays, the scholars introduce the complex-octonions to depict the electromagnetic and gravitational fields. And the complex-sedenions can be applied to study the field equations of the four interactions in the classical mechanics and quantum mechanics. Further, it is able to extend the field equations from the flat space into the curved space described with the complex-sedenions, by means of the tangent-frames and tensors. The research states that a few physical quantities will make a contribution to certain spatial parameters of the curved spaces. These spatial parameters may exert an influence on some operators (such as, divergence, gradient, and curl), impacting the field equations in the curved spaces, especially, the field equations of the four quantum-fields in the quantum mechanics. Apparently, the paper and General Relativity both confirm and succeed to the Cartesian academic thought of ‘the space is the extension of substance’.

A New Test of the Theory of General Relativity

1979 ◽  
Vol 3 (5) ◽  
pp. 364-364
Author(s):  
D. F. Crawford
Keyword(s):  
General Relativity ◽  
Space Time ◽  
Review Article ◽  
Curved Space ◽  
Gravitational Theories ◽  
Photon Frequency

It has been recently suggested (Crawford 1979) that there is an interaction between a photon and curved space-time that can be observed as a redshift of the photon frequency. Since the amount of the redshift is a function of the curvature it may be used to discriminate between gravitational theories. This is easily done using the parametrized post-Newtonian (PPN) limit fully described in the review article by Will (1972).

scholarly journals GRAVITY FROM DIRAC EIGENVALUES

1998 ◽  
Vol 13 (06) ◽  
pp. 479-494 ◽  
Author(s):  
GIOVANNI LANDI ◽  
CARLO ROVELLI
Keyword(s):  
General Relativity ◽  
Jacobian Matrix ◽  
Equations Of Motion ◽  
Scaling Law ◽  
Einstein Equations ◽  
Fermion Field ◽  
Spectral Action ◽  
Curved Space ◽  
Invariant Description ◽  
Infinite Set

We study a formulation of Euclidean general relativity in which the dynamical variables are given by a sequence of real numbers λn, representing the eigenvalues of the Dirac operator on the curved space–time. These quantities are diffeomorphism-invariant functions of the metric and they form an infinite set of "physical observables" for general relativity. Recent work of Connes and Chamseddine suggests that they can be taken as natural variables for an invariant description of the dynamics of gravity. We compute the Poisson brackets of the λn's, and find that these can be expressed in terms of the propagator of the linearized Einstein equations and the energy-momentum of the eigenspinors. We show that the eigenspinors' energy-momentum is the Jacobian matrix of the change of coordinates from the metric to the λn's. We study a variant of the Connes–Chamseddine spectral action which eliminates a disturbing large cosmological term. We analyze the corresponding equations of motion and find that these are solved if the energy momenta of the eigenspinors scale linearly with the mass. Surprisingly, this scaling law codes Einstein's equations. Finally we study the coupling to a physical fermion field.

BORN'S RECIPROCAL GENERAL RELATIVITY THEORY AND COMPLEX NON-ABELIAN GRAVITY AS GAUGE THEORY OF THE QUAPLECTIC GROUP: A NOVEL PATH TO QUANTUM GRAVITY

2008 ◽  
Vol 23 (10) ◽  
pp. 1487-1506 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
General Relativity ◽  
Gauge Theory ◽  
Planck Scale ◽  
Relativity Theory ◽  
Target Space ◽  
Speed Limit ◽  
General Relativity Theory ◽  
Curved Space ◽  
Maximal Speed ◽  
Proper Force

Born's reciprocal relativity in flat space–times is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved space–times and construct a reciprocal general relativity theory (in curved space–times) as a local gauge theory of the quaplectic group and given by the semidirect product [Formula: see text], where the non-Abelian Weyl–Heisenberg group is H(1, 3). The gauge theory has the same structure as that of complex non-Abelian gravity. Actions are presented and it is argued why such actions based on Born's reciprocal relativity principle, involving a maximal speed limit and a maximal proper force, is a very promising avenue to quantize gravity that does not rely in breaking the Lorentz symmetry at the Planck scale, in contrast to other approaches based on deformations of the Poincaré algebra, quantum groups. It is discussed how one could embed the quaplectic gauge theory into one based on the U(1, 4), U(2, 3) groups where the observed cosmological constant emerges in a natural way. We conclude with a brief discussion of complex coordinates and Finsler spaces with symmetric and nonsymmetric metrics studied by Eisenhart as relevant closed-string target space backgrounds where Born's principle may be operating.

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