Examples
Noteworthy examples of vacuum solutions, electrovacuum solutions, and so forth, are listed in specialized articles (see below). These solutions contain at most one contribution to the energy-momentum tensor, due to a specific kind of matter or field. However, there are some notable exact solutions which contain two or three contributions, including:
- NUT-Kerr–Newman–de Sitter solution contains contributions from an electromagnetic field and a positive vacuum energy, as well as a kind of vacuum perturbation of the Kerr vacuum which is specified by the so-called NUT parameter,
- Gödel dust contains contributions from a pressureless perfect fluid (dust) and from a positive vacuum energy.
Some hypothetical possibilities which don't fit into our rough classification are:
- certain wormhole metrics (which can serve as a speculative toy model of a stargate held open by a hypothetical kind of exotic matter, as in 2001: A Space Odyssey; also a toy model of hypothetical time machine, see below),
- Alcubierre metric (which has been used as a speculative toy model of effectively superluminal space travel, as in the warp drive from Star Trek).
- "Time machines", i.e. initially nice spacetimes in which at some stage of evolution closed causal curves appear.
Some doubt has been cast upon whether sufficient quantity of exotic matter needed for wormholes and Alcubierre bubbles can exist. Later, however, these doubts were shown to be mostly groundless. The third of these examples, in particular, is an instructive example of the procedure mentioned above for turning any Lorentzian manifold into a "solution". It is along this way that Hawking succeeded in proving that time machines of a certain type (those with a "compactly generated Cauchy horizon") cannot appear without exotic matter. Such spacetimes are also a good illustration of the fact that unless a spacetime is especially nice ("globally hyperbolic") the Einstein equations do not determine its evolution uniquely. Any spacetime may evolve into a time machine, but it never has to do so.
Read more about this topic: Exact Solutions In General Relativity
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—G.C. (Georg Christoph)
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