publication . Preprint . Article . 2012

The Riemann-Lovelock Curvature Tensor

David Kastor;
Open Access English
  • Published: 02 Jul 2012
Abstract
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 prop...
Subjects
arXiv: General Relativity and Quantum Cosmology
free text keywords: High Energy Physics - Theory, Physics and Astronomy (miscellaneous), Scalar curvature, Weyl tensor, symbols.namesake, symbols, Symmetric tensor, Riemann curvature tensor, Tensor density, Physics, Metric tensor (general relativity), Einstein tensor, Classical mechanics, Ricci decomposition

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publication . Preprint . Article . 2012

The Riemann-Lovelock Curvature Tensor

David Kastor;