D-DIMENSIONAL GRAVITY FROM (D+1) DIMENSIONS

We generalize Wesson's procedure, whereby vacuum (4 + 1)-dimensional f ield equations give rise to (3 + 1)-dimensional equations with sources , to arbitrary dimensions. We then employ this generalization to relat e the usual (3 + 1)-dimensional vacuum field equations to (2 + 1)-dime nsional field equations with sources and derive the analogues of the c lasses of solutions obtained by Pence de Leon. This way of viewing low er dimensional gravity theories can be of importance in establishing a relationship between such theories and the usual four-dimensional gen eral relativity, as well as giving a way of producing exact solutions in (2 + 1) dimensions that are naturally related to the vacuum (3 + 1) -dimensional solutions. An outcome of this correspondence, regarding t he nature of lower dimensional gravity, is that the intuitions obtaine d in (3 + 1) dimensions may not be automatically transportable to lowe r dimensions. We also extend a number of physically motivated solution s studied by Wesson and Pence de Leon to (D + 1) dimensions and employ the equivalence between the (D + 1) Kaluza-Klein theories with empty D-dimensional Brans-Dicke theories (with omega = 0) to throw some ligh t on the solutions derived by these authors.