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# General relativity

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Theory published by Albert Einstein in 1915. It gives a geometrical explanation of gravity, where the energy-matter content of the universe determines its curvature, and a particle subject to no non-gravitational forces follows a path of extremal length in that curved surface. The way the energy-matter content and the curvature relate to each other is given by the field equations,

  Rik - 1/2 gik R + Λ gik = 8 π G/c4 Tik

where Rik is the Ricci curvature tensor, R is the Ricci curvature scalar, gik is the metric tensor, Λ is the cosmological constant, and Tik is the stress-energy tensor. gik is a symmetric tensor of 4 x 4, so it has 10 components. Given the freedom of choice of coordinates the independent equations reduce to 6.

In the case of no curvature, the theory reduces itself to special relativity, published by Einstein a decade before.

Einstein realized that the theory in his original formulation didn't have a static solution when applied to the whole universe: in other words, the universe should be either expanding or contracting. This sufficiently distressed Einstein that he put an extra tweak in the model, the [cosmological constant]? Λ to adjust for this, but even with that additional term the static solution is unstable. A decade later, though, [Edwin Hubble]? proved that the universe is indeed expanding, and the adjustment was gladly abandoned. Since then, the cosmological constant has been in and out of fashion. As of this writing (middle of 2001), there seems to be increasing experimental evidence that the cosmological constant is needed to explain observations.

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Last edited July 26, 2001 2:49 pm (diff)
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