Lovelock Tensor as Generalized Einstein Tensor
نویسنده
چکیده
We show that the splitting feature of the Einstein tensor, as the first term of the Lovelock tensor, into two parts (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 which can be spanned linearly in terms of homogeneous tensors. As an example, we demonstrate this analogy for the Lovelock tensor. s1Introduction
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