Einstein-Hilbert action with cosmological term from Chern-Simons gravity

摘要

We propose a modification to the Lie algebra S-expansion method. The modification is carried out by imposing a condition on the S-expansion procedure, when the semigroup is given by a cyclic group of even order. The S-expanded algebras are called S-H-expanded algebras where S = Z(2n). The invariant tensors for S-H-expanded algebras are calculated and the dual formulation of S-H-expansion procedure is proposed. We consider the S-H-expansion of the five-dimensional AdS algebra and its corresponding invariants tensors are found. Then a Chern-Simons Lagrangian invariant under the five-dimensional AdS algebra S-H-expanded is constructed and its relationship to the general relativity is studied. (C) 2014 Elsevier B.V. All rights reserved.