Lanczos-Lovelock-Cartan gravity from Clifford-space geometry

Abstract:

A rigorous construction of Clifford-space (C-space) gravity is presented which is compatible with the Clifford algebraic structure and permits the derivation of the expressions for the connections with torsion in C-spaces. The C-space generalized gravitational field equations are derived from a variational principle based on the extension of the Einstein-Hilbert-Cartan action. We continue by arguing how Lanczos-Lovelock-Cartan (LLC) higher curvature gravity with torsion can be embedded into gravity in C-spaces and suggest how this might also occur for extended gravitational theories based on f(R), f(R μν), ... actions, for polynomial-valued functions. In essence, the LLC curvature tensors appear as Ricci-like traces of certain components of the C-space curvatures. Torsional gravity is related to higher-order corrections of the bosonic string-effective action. In the torsionless case, black-strings and black-brane metric solutions in higher dimensions D > 4 play an important role in finding specific examples of solutions to LL gravity. © 2013 World Scientific Publishing Company.

Año de publicación:

2013

Keywords:

• Lanczos-Lovelock-Cartan gravity
• Clifford algebras

Fuente:

scopus