BTZ black holes from the five-dimensional general relativity with a negative cosmological constant

We show that the five-dimensional general relativity with a negative cosmological constant allows the solutions of the form M3×Mg where M3 is the three-dimensional BTZ black hole and Mg is a higher genus (g>1) Riemann surface with a fixed size. It is shown that this type of spontaneous compactification on a Riemann surface is possible only for the genus larger than one. From type IIB string theory point of view, certain near horizon geometry of D three-branes wrapped on the compact Riemann surface (g>1) is the BTZ (or AdS3) space-time tensored with the Riemann surface and a constant size five-sphere. The relevance of our analysis to the positive energy conjecture of Horowitz and Myers is discussed.