scholarly journals Quaternionic Variational Formalism for General Relativity in Riemann and Riemann-Cartan Space-Times

2012 ◽  
Vol 128 (6) ◽  
pp. 1107-1139
Author(s):  
K. Morita
Author(s):  
F. P. POULIS ◽  
J. M. SALIM

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl geometry and it is shown that it gives extra contributions to the trajectories of test particles, serving as one more motivation to study general relativity in Weyl geometry. It is introduced its variational formalism and it is established the coupling with other physical fields in such a way that the theory acquires a gauge symmetry for the geometrical fields. It is shown that this symmetry is still present for the red-shift and it is concluded that for cosmological models it opens the possibility that observations can be fully described by the new geometrical scalar field. It is concluded then that this reformulation, although representing a theoretical advance, still needs a complete description of their objects.


Author(s):  
M. P. Hobson ◽  
G. P. Efstathiou ◽  
A. N. Lasenby
Keyword(s):  

2012 ◽  
Vol 182 (8) ◽  
pp. 894 ◽  
Author(s):  
Vladimir N. Lukash ◽  
Elena V. Mikheeva ◽  
Vladimir N. Strokov
Keyword(s):  

2015 ◽  
Vol 8 (2) ◽  
pp. 2135-2147 ◽  
Author(s):  
C. Y. Lo

General relativity is incomplete since it does not include the gravitational radiation reaction force and the interaction of gravitation with charged particles. General relativity is confusing because Einstein's covariance principle is invalid in physics. Moreover, there is no bounded dynamic solution for the Einstein equation. Thus, Gullstrand is right and the 1993 Nobel Prize for Physics press release is incorrect. Moreover, awards to Christodoulou reflect the blind faith toward Einstein and accumulated errors in mathematics. Note that the Einstein equation with an electromagnetic wave source has no valid solution unless a photonic energy-stress tensor with an anti-gravitational coupling is added. Thus, the photonic energy includes gravitational energy. The existence of anti-gravity coupling implies that the energy conditions in space-time singularity theorems of Hawking and Penrose cannot be satisfied, and thus are irrelevant. Also, the positive mass theorem of Yau and Schoen is misleading, though considered as an achievement by the Fields Medal. E = mc2 is invalid for the electromagnetic energy alone. The discovery of the charge-mass interaction establishes the need for unification of electromagnetism and gravitation and would explain many puzzles. Experimental investigations for further results are important.


Sign in / Sign up

Export Citation Format

Share Document