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*four-momentum*but am not certain what it actually calculates. Maybe I just don't know it and there is yet an equation for this.

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- Thread starter tgramling
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Check out the curvature tensor.

http://en.wikipedia.org/wiki/Einstein_tensor

http://en.wikipedia.org/wiki/Einstein_tensor

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Ich

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In certain symmetric conditions, the field equations are a lot simpler. Check out http://math.ucr.edu/home/baez/einstein/einstein.html" [Broken].

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George Jones

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four-momentumbut am not certain what it actually calculates. Maybe I just don't know it and there is yet an equation for this.

The link that FunkyDwarf tell only half the story, the geometry and curvature part. The other half of the story is the energy/mass/momentum part, and this, too is described by a tensor, the energy-momentum (sometime called stress-energy tensor).

Einstein's equation of general relativity sets theses two tensors "equal", so that curvature and geometry equals distribution of energy/mass/momentum. Since this is an equation, it is impossible to change just one side: change the geometry side and this means that distribution of energy/mass/momentum must salso be changed; change the distribution of energy/mass/momentum, and this means geometry must also be changed.

This is the equation that Ich's link discusses; see also

http://en.wikipedia.org/wiki/Einstein_field_equations.

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Ok, so I now have the equation, thank you guys very much for that by the way, but now can anyone tell me how to apply it? It would seem simple enough as it is looks to serve like a function almost, but for every constant there are numerous other constants involved. What I am asking here is if I MUST go down the chain of constants in order to arrive upon my final answer

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Ich

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I gave you a link. I don't think you'll find anything more appropriate for your purposes.do you know if there is an example or if you can give me one of a highly symmetric situation?

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The main problem with non-linear equations is that you cannot just add up two solutions to get a third solution. For example, the Schwarzschild solution is a good description of the spacetime around the earth and it is also a good description of the spacetime around the moon, but if you want a the spacetime around the earth-moon system you cannot simply add the two Schwarzschild solutions to get the right answer.

For the most important examples of highly symmetric solutions look up: Schwarzschild metric, Kerr metric, and FLRW metric.

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Fredrik

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The equation is extremely difficult to solve. For example, the Kerr metric, which describes a universe that's completely empty except for a single rotating star or black hole with no electric charge, wasn't found until 1963. In other words, it took 48 years to find that solution, even though it describes one of those "highly symmetric situations".

The first solutions that were found are even simpler. The Schwarzschild metric was found in 1915 and describes a universe that's completely empty except for a single

Some of the FLRW solutions are very accurate descriptions of the large-scale behavior of the universe. That last claim is often called "the big bang theory", because all the FLRW solutions have a property called an "initial singularity" or a "big bang".

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George Jones

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The Einstein equation is a single tensor equation that is equivalent to a set of ten coupled non-linear partial differential equations. Without symmetry, this is as bad (or worse!) than it sounds.

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malawi_glenn

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However, for a good explanation of the theoretical underpinning, check out Leonard Susskind's lectures on GR at YouTube or iTunes

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(42-6). The excess radius is MG/3c^2 ... so for example if you wanted to know how much the mass of the earth curves space you can make a quick calculation and see that its in the range of a one millimeter

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