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Physics
Special and General Relativity
Black Hole & Spacetime Curvature: Can Mass Decrease It?
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[QUOTE="pervect, post: 5496178, member: 14402"] Spacetime curvature is not represented by a single number, but a rather complex structure consisting of many numbers which are called "components" of the spacetime curvature. There isn't any clear meaning to "decreasing" or "increasing" a set of numbers. What do you call it if one member of the set increases, while the other decreases? To take a simple example, it's not meaningful to ask whether [1,1] is "greater" or "lesser" than [2, 1/2], though one can meaningfully say they aren't equal. There are some additional complexities. The set of numbers that completely describes spacetime curvature is called the Riemann curvature tensor. There are other smaller sets of numbers that also describe spacetime curavature that are important to the theory that are not, however, as complete as the Riemann tensor, but the term "spacetime curvature" is sufficiently vague that it's not clear which set of numbers one is talking about. For the time being, though, we can simplify things by assuming that one is talking about the most complete representation of spacetime curvature, the full set of numbers in the Riemann tensor, and not some important but less general set. Description of the "mass" of some collection of matter is not, by itself, sufficient to compute all the numbers in the Riemann tensor. One needs additional information about the composition of the matter, for instance it's momentum, and the value of any internal pressures, to compute the Riemann tensor. [/QUOTE]
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Physics
Special and General Relativity
Black Hole & Spacetime Curvature: Can Mass Decrease It?
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