From Riemannian Geometry to Einstein’s General Relativity Theory and Beyond: Space-Time Structures, Geometrization and Unification

2006 ◽  
Author(s):  
Luciano Boi
Keyword(s):  
General Relativity ◽  
Riemannian Geometry ◽  
Space Time ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Time Structures ◽  
Einstein’S General Relativity

GENERAL RELATIVITY AND SECTIONAL CURVATURE

2006 ◽  
Vol 03 (05n06) ◽  
pp. 1077-1087
Author(s):  
G. S. HALL
Keyword(s):  
General Relativity ◽  
Vector Field ◽  
Sectional Curvature ◽  
Relativity Theory ◽  
Curvature Function ◽  
Smooth Vector ◽  
General Relativity Theory ◽  
Metric Tensor ◽  
Algebraic Properties ◽  
Einstein’S General Relativity

A discussion is given of the sectional curvature function on a four-dimensional Lorentz manifold and, in particular, on the space–time of Einstein's general relativity theory. Its tight relationship to the metric tensor is demonstrated and some of its geometrical and algebraic properties evaluated. The concept of a sectional curvature preserving symmetry, in the form of a certain smooth vector field, is introduced and discussed.

On the differential topology of space-time

1971 ◽  
Vol 69 (2) ◽  
pp. 295-296 ◽  
Author(s):  
J. Wolfgang Smith
Keyword(s):  
General Relativity ◽  
Life History ◽  
Space Time ◽  
Average Density ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Differential Topology ◽  
Cosmology Theory ◽  
History Of

It has often been assumed in cosmology theory(1) that there exists an average density of matter in space which is everywhere greater than zero. Under this assumption the space-time M will be foliated by curves each of which represents the life history of a particle. In keeping with the postulates of general relativity theory we shall refer to these curves as geodesics. Letting X denote the space of particles one obtains a projection f: M → X which assigns to every P ∈ M the particle found at P. Conversely, given the projection f:M → X, one can recover the geodesics: they are precisely the fibres f−1(x), x∈X.

scholarly journals Possible Unification of Quantum Mechanics and General Relativity Theory Based on the Three-Dimensional Quantized Spaces

2018 ◽  
Author(s):  
Jae-Kwang Hwang
Keyword(s):  
General Relativity ◽  
Wave Function ◽  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Energy Transition ◽  
Space Time ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Dimensional Space Time

Three-dimensional quantized space model is newly introduced. Quantum mechanics and relativity theory are explained in terms of the warped three-dimensional quantized spaces with the quantum time width (Dt=tq). The energy is newly defined as the 4-dimensional space-time volume of E = cDtDV in the present work. It is shown that the wave function of the quantum mechanics is closely related to the warped quantized space shape with the space time-volume. The quantum entanglement and quantum wave function collapse are explained additionally. The special relativity theory is separated into the energy transition associated with the space-time shape transition of the matter and the momentum transition associated with the space-time location transition. Then, the quantum mechanics and the general relativity theory are about the 4-dimensional space-time volume and the 4-dimensional space-time distance, respectively.

scholarly journals Einstein’s Notational Equation of Electro-Magnetic Field Equation in Rindler spacetime

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Magnetic Field ◽  
General Relativity ◽  
Field Equation ◽  
Electromagnetic Fields ◽  
Space Time ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Electro Magnetic Field ◽  
Rindler Space ◽  
Electro Magnetic

We find Einstein’s notational equation of the electro-magnetic field equation and the electromagneticfield in Rindler space-time. Because, electromagnetic fields of the accelerated frame include in general relativity theory.

scholarly journals Do Child Abuse Pediatricians Search for a “Pediatric Vulcan Planet”? Comparison of Controversies about the Vulcan-Must-Exist-Theory and the Infant-Must-Have-Been-Shaken-Theory

2020 ◽  
Vol 3 (2) ◽  
pp. p162
Author(s):  
Niels Lynøe ◽  
Niklas Juth ◽  
Chris B Brook ◽  
Anders Eriksson
Keyword(s):  
General Relativity ◽  
Child Abuse ◽  
Head Trauma ◽  
Abusive Head Trauma ◽  
The Other ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
The One ◽  
Legal Consequences ◽  
Einstein’S General Relativity

We argue that there are similarities between the Vulcan-must-exist-theory, derived from the Original Unrestricted Newtonian Gravitational (OUNG) theory, on the one hand, and on the other hand the infant-must-have-been-shaken-theory, derived from the Original Unrestricted Abusive Head Trauma (OUAHT) theory. Although the Vulcan-must–exist-theory was apparently supported by observations over a period of 50 years, after the introduction of Einstein’s general relativity theory in 1915 and its corroboration in 1919, the alleged planet was subsequently neither observed nor needed. In analogy with the Einstein/Vulcan reasoning, we suggest that the introduction of the non-shaken baby theory by Geddes et al. in 2001-2004 indicates that in cases where an infant displays no external signs of trauma, the infant-must-have-been-shaken-theory is no longer needed. Moreover we argue that the two new theories -Einstein’s and Geddes et al.’s- have relevant similarities in terms of the effect on the respective original, unrestricted theory. Just as acceptance of Einstein’s general relativity theory led to the abandonment of the Vulcan-must-exist-theory, it is reasonable to claim that the infant-must-have-been-shaken-theory should also be abandoned. We finally argue that while the consequences of abandoning the Vulcan-must-exist-theory were restricted to some scientific and astronomical issues, the infant-must-have-been-shaken-theory has not yet been abandoned because of the societal and legal consequences.

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