scholarly journals HOMOGENEOUS SOLUTIONS OF QUADRATIC GRAVITY

2011 ◽  
Vol 03 ◽  
pp. 111-120 ◽  
Author(s):  
DANIEL MÜLLER
Keyword(s):  
Relativity Theory ◽  
General Relativity Theory ◽  
Homogeneous Solutions ◽  
Bianchi I ◽  
Quadratic Theory ◽  
Quadratic Gravity ◽  
Generalized Potential ◽  
Planck Time ◽  
Limiting Case ◽  
Einstein’S General Relativity

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. In this work we present the 3 + 1 decomposition for the zero vorticity case for arbitrary spatially homogenous spaces. We specialize for the particular Bianchi I diagonal case. The 3- curvature can be understood as a generalized potential, and the Bianchi I case is a limiting case where this potential is negligible to the dynamics. The spirit should be analogous, in some sense to the BKL solution. In this sense, a better understanding of the Bianchi I case could shed some light into the general Bianchi case.

scholarly journals BIANCHI I SOLUTIONS OF EFFECTIVE QUADRATIC GRAVITY

2012 ◽  
Vol 21 (04) ◽  
pp. 1250037 ◽  
Author(s):  
DANIEL MÜLLER ◽  
JULIANO A. DE DEUS
Keyword(s):  
Numerical Solutions ◽  
Relativity Theory ◽  
De Sitter ◽  
General Relativity Theory ◽  
Spatial Metrics ◽  
Effective Gravity ◽  
Bianchi I ◽  
Quadratic Theory ◽  
Quadratic Gravity ◽  
Planck Time

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model E3 for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity. This work is a generalization for nondiagonal spatial metrics of a previous result obtained by one of us and a collaborator for Bianchi I spaces.

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.

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.

scholarly journals Does Special Relativity Lead to a Trans-Planckian Crisis?

2019 ◽  
Vol 12 (1) ◽  
pp. 1
Author(s):  
Espen Gaarder Haug
Keyword(s):  
Special Relativity ◽  
Gravitational Constant ◽  
Maximum Velocity ◽  
Relativity Theory ◽  
Speed Limit ◽  
Planck Length ◽  
Planck Constant ◽  
General Relativity Theory ◽  
Time Intervals ◽  
Planck Time

In gravity theory, there is a well-known trans-Planckian problem, which is that general relativity theory leads to a shorter than Planck length and shorter than Planck time in relation to so-called black holes. However, there has been little focus on the fact that special relativity also leads to a trans-Planckian problem, something we will demonstrate here. According to special relativity, an object with mass must move slower than light, but special relativity has no limits on how close to the speed of light something with mass can move. This leads to a scenario where objects can undergo so much length contraction that they will become shorter than the Planck length as measured from another frame, and we can also have shorter time intervals than the Planck time. The trans-Planckian problem is easily solved by a small modification that assumes Haug’s maximum velocity for matter is the ultimate speed limit for something with mass. This speed limit depends on the Planck length, which can be measured without any knowledge of Newton’s gravitational constant or the Planck constant.

Einstein’s General Relativity Theory

2019 ◽  
pp. 329-388
Author(s):  
Helmut Günther ◽  
Volker Müller
Keyword(s):  
General Relativity ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Einstein’S General Relativity
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