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Field equations: The field equations in physics are a set of equations that describe the relationship between matter and spacetime. They are the fundamental equations of general relativity, and they were first proposed by Albert Einstein in 1915. See also Theory of Relativity, Space time, Matter, Space, Time.
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Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

 
Author Concept Summary/Quotes Sources

Bernulf Kanitscheider on Field Equations - Dictionary of Arguments

I 178
Gravity/Relativity/Kanitscheider: A world filled with gravitational radiation cannot be completely flat. However, the wave is damped by becoming energetically poorer. So a black hole can arise by the self-interaction at the end.
One has found strict solutions of the field equations for closed universes whose sole content consists of gravitational waves.
Here, the curvature of spacetime itself must form the principium individuationis.

Field equation:

(4) Rμν - 1/2 gμνR + λ gμν = 8πGTμν

left side: phenomena, curvature.
right side: matter, cause, pressure, density, tension, charge.
Field equation: If formulated as tensor equation, the curvature (and therefore the gravity) disappears in the outer space of the sun. Therefore Einstein uses the Ricci tensor and the curvature scalar R, both contain only the contribution of the local matter.
The coupling constant G is not determined by the field equations themselves, but must be determined externally empirically. It does not belong to the nomological but to the contingent elements of the theory.

Notation:
Rμν: Riccitensor
R: Curvature scalar
Tμν: Matter tensor
>Space curvature/Kanitscheider
, >Universe/Kanitscheider, >Relativity theory.
I 182
Field equations/channel separators: in their above form they always contain all kinds of spacetimes. Here it is necessary to specify the boundary conditions which separate the local solutions from the global solutions useful in cosmology.
Here, at great distance, the spacetime structure merges into the asymptotically flat Minkowski space. This is unsatisfactory, because it allows an excellent observer point of view, in contradiction with the accepted Copernican world view.
((s) asymptotically flat/(s): means that in the outskirts of the universe it is different from us. No life is possible there. Therefore designated observer point of view).
>Minkowski space.

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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Kanitsch I
B. Kanitscheider
Kosmologie Stuttgart 1991

Kanitsch II
B. Kanitscheider
Im Innern der Natur Darmstadt 1996


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