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The Riemann-Lovelock Curvature Tensor
Classical and Quantum Gravity (2012)
  • David Kastor, University of Massachusetts - Amherst

In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \le D <4k. In D=2k+1 this identity implies that all solutions of pure kth-order Lovelock gravity are `Riemann-Lovelock' flat. It is verified that the static, spherically symmetric solutions of these theories, which are missing solid angle space times, indeed satisfy this flatness property. This generalizes results from Einstein gravity in D=3, which corresponds to the k=1 case. We speculate about some possible further consequences of Riemann-Lovelock curvature.

Publication Date
February 23, 2012
Publisher Statement
This is the pre-published version harvested from arXiv. The published version is located at
Citation Information
David Kastor. "The Riemann-Lovelock Curvature Tensor" Classical and Quantum Gravity Vol. 29 Iss. 15 (2012)
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