Three-dimensional classical spacetimes

The authors extend what is known about the structure of (2+1)-dimensional gravitational field theories. The non-existence of any Newtonian limit to these theories is investigated in the presence of Brans-Dicke scalar fields and non-linear curvature terms in the gravitational action. A number of new exact static and non-static solutions of (2+1) general relativity with scalar field, perfect fluid and magnetic field sources are presented and studied in detail. Some of these possess a correspondence with (3+1) solutions of general relativity through a Kaluza-Klein type reduction and exhibit the 'wedge' structure of (3+1)-dimensional solutions describing line sources like vacuum strings. An algebraic classification of (2+1) gravitational fields is derived using the Bach-Weyl tensor. The description of the general cosmological solution is given in terms of arbitrary spatial functions independently specified on a spacelike surface of constant time together with a series approximation to spacetime in the vicinity of a general cosmological singularity.