scholarly journals Christoffel Symbols and Chiral Properties of the Space-Time Geometry for the Atomic Electron States

2021 ◽  
Vol 12 (04) ◽  
pp. 483-512
Author(s):  
Claude Daviau ◽  
Jacques Bertrand
Author(s):  
Irina Rozgacheva

Huge filaments with scales from several hundred megaparsecs to gigaparsecs are detected in the distribution of galaxies and clusters, quasars, gamma-bursters. The hypothesis on the nature of the huge filaments as regions of space-time deformation is proposed. An anisotropic deformation of the local region is described by the strain tensor, it depends on the velocities of matter. Galaxies get an extra velocity in the region, which leads to the formation of filamentary structures. The class of exact solution of the GR equations is constructed by introducing the special definition of the Christoffel symbols as function of the velocity of matter. With a definition of these symbols, the motion matter equation turns into identity. For the sake of simplicity, an ideal fluid is considered.


2020 ◽  
Author(s):  
Swagatam Sen

Focus of this study is to explore some aspects of mathematical foundations for using complex manifolds as a model for space-time. More specifically, certain equations of motions have been derived as a Projective geodesic on a real manifold embedded within a complex one. To that goal, first the geodesic on complex manifold has been computed using local complex and conjugate coordinates, and then its projection on the real sub-manifold has been studied. The projective geodesic, thus obtained, is shown to have additional terms beyond the usual Christoffel symbols, and hence expands the geodesic to capture effects beyond the mere gravitational ones.


2002 ◽  
Author(s):  
J. B. Kennedy
Keyword(s):  

Author(s):  
Roger Penrose ◽  
Wolfgang Rindler
Keyword(s):  

2018 ◽  
Vol 77 (4) ◽  
pp. 173-184
Author(s):  
Wenxing Yang ◽  
Ying Sun

Abstract. The causal role of a unidirectional orthography in shaping speakers’ mental representations of time seems to be well established by many psychological experiments. However, the question of whether bidirectional writing systems in some languages can also produce such an impact on temporal cognition remains unresolved. To address this issue, the present study focused on Japanese and Taiwanese, both of which have a similar mix of texts written horizontally from left to right (HLR) and vertically from top to bottom (VTB). Two experiments were performed which recruited Japanese and Taiwanese speakers as participants. Experiment 1 used an explicit temporal arrangement design, and Experiment 2 measured implicit space-time associations in participants along the horizontal (left/right) and the vertical (up/down) axis. Converging evidence gathered from the two experiments demonstrate that neither Japanese speakers nor Taiwanese speakers aligned their vertical representations of time with the VTB writing orientation. Along the horizontal axis, only Japanese speakers encoded elapsing time into a left-to-right linear layout, which was commensurate with the HLR writing direction. Therefore, two distinct writing orientations of a language could not bring about two coexisting mental time lines. Possible theoretical implications underlying the findings are discussed.


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