The significance of curvature in general relativity
- Cite this article as:
- Hall, G.S. Gen Relat Gravit (1984) 16: 495. doi:10.1007/BF00762342
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In General Relativity, one has several traditional ways of interpreting the curvature of spacetime, expressed either through the curvature tensor or the sectional curvature function. This essay asks what happens if curvature is treated on a more primitive level, that is, if the curvature is prescribed, what information does one have about the metric and associated connection of space-time? It turns out that a surprising amount of information is available, not only about the metric and connection, but also, through Einstein's equations, about the algebraic structure of the energy-momentum tensor.