Lovelock tensor as generalized Einstein tensor
Abstract
We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts, namely the Ricci tensor and the term proportional to the curvature scalar, with the trace relation between them is a common feature of any other homogeneous terms in the Lovelock tensor. Motivated by the principle of general invariance, we find that this property can be generalized, with the aid of a generalized trace operator which we define, for any inhomogeneous Euler Lagrange expression that can be spanned linearly in terms of homogeneous tensors. Then, through an application of this generalized trace operator, we demonstrate that the Lovelock tensor analogizes the mathematical form of the Einstein tensor, hence, it represents a generalized Einstein tensor. Finally, we apply this technique to the scalar Gauss Bonnet gravity as an another version of string inspired gravity.
 Publication:

General Relativity and Gravitation
 Pub Date:
 January 2009
 DOI:
 10.1007/s1071400806589
 arXiv:
 arXiv:grqc/9510060
 Bibcode:
 2009GReGr..41..117F
 Keywords:

 Higher order gravity;
 Lovelock Einstein tensors;
 Trace operator;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 16 pages, added refs., corrected a mistyped eq. (the last one in p12), TeX file (using phyzzx.tex)