Flat-space metric in the quaternion formulation of general relativity

1969 ◽  
Vol 63 (1) ◽  
pp. 318-330
Author(s):  
C. Marcio do Amaral ◽  
C. G. Oliveira
Keyword(s):  
General Relativity ◽  
Flat Space

THE GRAVITATIONAL ORIGIN OF THE DISTINCTION BETWEEN SPACE AND TIME

2009 ◽  
Vol 18 (14) ◽  
pp. 2155-2158 ◽  
Author(s):  
ASHER YAHALOM
Keyword(s):  
General Relativity ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Flat Space ◽  
Gravitational Theory ◽  
Clear Distinction ◽  
Temporal Dimension ◽  
Spatial Dimensions ◽  
Standard Presentation

To the ordinary human it is obvious that there is a clear distinction between the spatial dimensions, in which one can go either way, and the temporal dimension, in which one seems only to move forward. But the uniqueness of time is also rooted in the standard presentation of general relativity, in which the metric of space–time is locally Lorentzian, i.e. ημν = diag (1, -1, -1, -1). This is presented as an independent axiom of the theory, which cannot be deduced. In this essay I will claim otherwise. I will show that the existence of time should not be enforced on the gravitational theory of general relativity but rather should be deduced from it. The method of choice is linear stability analysis of flat space–times.

scholarly journals Rotating Melvin-like Universes and Wormholes in General Relativity

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1306
Author(s):  
Kirill Bronnikov ◽  
Vladimir Krechet ◽  
Vadim Oshurko
Keyword(s):  
Magnetic Field ◽  
General Relativity ◽  
Equation Of State ◽  
Symmetry Axis ◽  
Energy Condition ◽  
Flat Space ◽  
Stiff Matter ◽  
Cylindrically Symmetric ◽  
The One ◽  
The Magnetic Field

We find a family of exact solutions to the Einstein–Maxwell equations for rotating cylindrically symmetric distributions of a perfect fluid with the equation of state p=wρ (|w|<1), carrying a circular electric current in the angular direction. This current creates a magnetic field along the z axis. Some of the solutions describe geometries resembling that of Melvin’s static magnetic universe and contain a regular symmetry axis, while some others (in the case w>0) describe traversable wormhole geometries which do not contain a symmetry axis. Unlike Melvin’s solution, those with rotation and a magnetic field cannot be vacuum and require a current. The wormhole solutions admit matching with flat-space regions on both sides of the throat, thus forming a cylindrical wormhole configuration potentially visible for distant observers residing in flat or weakly curved parts of space. The thin shells, located at junctions between the inner (wormhole) and outer (flat) regions, consist of matter satisfying the Weak Energy Condition under a proper choice of the free parameters of the model, which thus forms new examples of phantom-free wormhole models in general relativity. In the limit w→1, the magnetic field tends to zero, and the wormhole model tends to the one obtained previously, where the source of gravity is stiff matter with the equation of state p=ρ.

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.

scholarly journals THE FLUCTUATION SPECTRA AROUND A GAUSSIAN CLASSICAL SOLUTION OF A TENSOR MODEL AND THE GENERAL RELATIVITY

2008 ◽  
Vol 23 (05) ◽  
pp. 693-718 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
General Relativity ◽  
Classical Solution ◽  
Flat Space ◽  
Effective Field ◽  
Tensor Model ◽  
Metric Tensor ◽  
Four Dimensions ◽  
Tensor Models ◽  
Momentum Spectra ◽  
General Coordinate Transformation

Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this paper, I study numerically the fluctuation spectra around a Gaussian classical solution of a tensor model, which represents a fuzzy flat space in arbitrary dimensions. It is found that the momentum distribution of the low-lying low-momentum spectra is in agreement with that of the metric tensor modulo the general coordinate transformation in the general relativity at least in the dimensions studied numerically, i.e. one to four dimensions. This result suggests that the effective field theory around the solution is described in a similar manner as the general relativity.

On the relativistic interpretation of astronomical observations

1959 ◽  
Vol 252 (1271) ◽  
pp. 476-487 ◽  
Keyword(s):  
Differential Equation ◽  
General Relativity ◽  
Apparent Motion ◽  
Flat Space ◽  
Frame Of Reference ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Astronomical Observations ◽  
Basic Ideas ◽  
Arbitrary Curvature

The basic ideas of apparent motion are formulated within the framework of general relativity theory. This requires the introduction of a dynamically meaningful frame of reference. A differential equation characterizing motion relative to this frame in a space of arbitrary curvature is formulated and its solutions for nearly flat space-time are obtained. These solutions are compared with the results of classical and special relativistic theory.

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’.

scholarly journals Variation of the Gravitational Constant in the Radiation-Dominated Universe

2012 ◽  
Vol 2012 ◽  
pp. 1-4
Author(s):  
L. L. Williams
Keyword(s):  
General Relativity ◽  
Scalar Field ◽  
Gravitational Constant ◽  
Flat Space ◽  
Scale Factor ◽  
Early History ◽  
Classical Electrodynamics ◽  
Field Equations ◽  
Walker Metric ◽  
History Of

The unification of classical electrodynamics and general relativity within the context of five-dimensional general relativity (Kaluza, 1921, and Thiry, 1948) contains a scalar field which may be identified with the gravitational constant, G. The field equations of this theory are solved under conditions of the Robertson-Walker metric for flat space, for a radiation-dominated universe—a model appropriate for the early history of our universe. This leads to a cosmology wherein G is inversely proportional to the Robertson-Walker scale factor. This result is discussed in the context of the Dirac large number hypothesis and in the context of an expression for G in terms of atomic constants.

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