EXACT-SOLUTIONS OF EINSTEIN AND EINSTEIN-SCALAR EQUATIONS IN 2+1 DIMENSIONS

A nonstatic and circularly symmetric exact solution of the Einstein eq uations (with a cosmological constant A and null fluid) in 2+1 dimensi ons is given. This is a nonstatic generalization of the uncharged spin less BTZ metric. For Lambda = 0, the spacetime is though not flat, the Kretschmann invariant vanishes. The energy, momentum, and power outpu t for this metric are obtained. Further a static and circularly symmet ric exact solution of the Einstein-massless scalar equations is given, which has a curvature singularity at r = 0 and the scalar field diver ges at r = 0 as well as at infinity.