Quote:
Originally Posted by Nesti
Yes, interesting indeed.
I said metric as a general comparison between all components within the Einstein Tensor...but if I must be specific, I would say that it is not the "components" either, I believe it would all come down to variations of the derivative values (1st and 2nd derivatives) held within the metric components. Of course the numbers of values vary depending upon how many dimensions we are talking about. 256 for a spacetime metric.
The "components" of the metric, are the mathematical operators, not the values themselves, true?
Cheers
Mark
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The number of components is based on the rank of the curvature tensor. For example the Riemann curvature tensor which has a rank of 4 has 4^4=256 components for 4 dimensional space.
The Ricci tensor which is a contracted version of the Riemann tensor has 2^4=16 components in 4 dimensional space. Taking into account symmetry the total number of components is 10.
Thus GR is a gravitational theory for 10 potentials (Newtonian theory has only 1 potential).
The Christoffel symbols in the Ricci or Einstein field equations result in the partial differentiation (1st and second order) of the each metric component. The metric component is the potential.
If the metric components are constant, the Christoffel symbols vanish and the metric is simply a geodesic or straight line in flat space.
Non vanishing Christoffel symbols (metric components are not constant) indicates curved geodesics.
Regards
Steven