X-Nico

Exact solutions in general relativity

With sufficiently clever assumptions of this sort, it is often possible to reduce the Einstein field equation to a much simpler system of equations, even a single partial differential equation (as happens in the case of stationary axisymmetric vacuum solutions, which are characterized by the Ernst equation) or a system of ordinary differential equations (as happens in the case of the Schwarzschild vacuum).

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Alcubierre metric (which has been used as a speculative toy model of effectively superluminal space travel, as in the warp drive from Star Trek).

see also