Exact lambdavacuum solutions in higher dimensions

Abstract In this work, we obtain exact solutions to the (n+2) -dimensional Einstein Field Equations with a non-zero cosmological constant for n ≥2. These solutions depend on a set Α of pairwise commuting constant matrices in sl ( n ,R), a constant matrix g 0 in I ( Α ), and a set of constant parameters. Different choices of Α , g 0 and the constant parameters correspond to different solutions. As examples, we show how to obtain the de Sitter metric, the Anti-de Sitter metric, the Birmingham metric, the Nariai metric, and the Anti-Nariai metric in higher dimensions, and construct a new solution. In addition, we study a solution in the context of cosmology.