Lovelock Tensor as Generalized Einstein Tensor

Details Lovelock Tensor as Generalized Einstein Tensor Lovelock Tensor as Generalized Einstein Tensor

1995-10-27

arxiv.org/abs/gr-qc/9510060v5

Gen.Rel.Grav.41:117-129,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, added refs., corrected a mistyped eq. (the last one in p12), TeX file (using phyzzx.tex)

Scientific paper

10.1007/s10714-008-0658-9

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.

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