Abstract
The Einstein--Hilbert action with a cosmological term is used to derive an action in 1+1 spacetime dimensions. It is shown that the two-dimensional theory is equivalent to planar symmetry in general relativity. The two-dimensional theory admits black holes and free dilatons, and has a structure similar to two-dimensional string theories. Since by construction these solutions also solve Einstein's equations, such a theory can bring two-dimensional results into the four-dimensional world. In particular the two-dimensional black hole is a black membrane in general relativity.
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