LOWER-DIMENSIONAL GRAVITY

Three-dimensional general relativity has many intriguing properties. Among them is a vanishing Newtonian potential which renders three-dimensional gravity nonattractive. An alternative (scalar-tensor) theory of three-dimensional gravity is obtained by dimensional reduction of four-dimensional general relativity. This theory admits a Newtonian limit and can further incorporate all the non-Newtonian objects such as gauge strings and global strings as well. Coupling with an electromagnetic field in three dimensions is also obtained by dimensional reduction and the result is found to be essentially different from the D=3 Maxwell-Einstein theory. The same approach is taken further in order to obtain a theory of gravity in two dimensions, where general relativity does not exist at all. The result is found to be very similar to two-dimensional dilaton gravity models proposed recently to study the end point of black hole evaporation. © 1994 The American Physical Society.