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S. Brian Edgar

Bio: S. Brian Edgar is an academic researcher from Linköping University. The author has contributed to research in topics: Weyl tensor & Riemann curvature tensor. The author has an hindex of 15, co-authored 58 publications receiving 580 citations.


Papers
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TL;DR: In this paper, the authors generalize Lovelock's results to trace-free (k, l)-forms, and give direct application to Maxwell, Lanczos, Ricci, Bel, and Bel-Robinson tensors.
Abstract: Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p⩾n. We generalize Lovelock’s results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrizing over n+1 indices, we establish a very general “master” identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel, and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.

59 citations

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TL;DR: By showing that all conformal Killing tensors are reducible in conformally flat spaces, this work has a method of constructing all conformityal Killing Tensors, and hence all the Killing tensor (which will in general be irreducible) of conformallyflat spaces using their conformalkilling vectors.
Abstract: Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors.

50 citations

Journal ArticleDOI
TL;DR: In this article, the authors generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, they establish a very general "master" identity for all trace-free (k, l)-forms.
Abstract: Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, we establish a very general 'master' identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.

40 citations

Journal ArticleDOI
TL;DR: The complete class of conformally flat, pure radiation metrics was given in this paper, generalizing the metric given recently by Wils, which is a generalization of Wils's pure radiation metric.
Abstract: The complete class of conformally flat, pure radiation metrics is given, generalizing the metric given recently by Wils.

33 citations

Journal ArticleDOI
TL;DR: In this paper, the authors show that the conformally flat, pure radiation metrics which are not plane waves are a larger class than Wils has obtained, and they show that such a metric is the only metric which admits no Killing vectors.
Abstract: Held has proposed an integration procedure within the GHP formalism built around four real, functionally independent, zero-weighted scalars. He suggests that such a procedure would be particularly simple for the `optimal situation', when the formalism directly supplies the full quota of four scalars of this type; a spacetime without any Killing vectors would be such a situation. Wils has recently obtained a metric which he claims is the only conformally flat, pure radiation metric which is not a plane wave; this metric has been shown by Koutras to admit no Killing vectors, in general. Therefore, as a simple illustration of the GHP integration procedure, we obtain systematically the complete class of conformally flat, pure radiation metrics. Our result shows that the conformally flat, pure radiation metrics, which are not plane waves, are a larger class than Wils has obtained.

26 citations


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Journal ArticleDOI
TL;DR: In this article, the authors present explicit models for a symmetry breakdown in the cases of the Weyl (or homothetic) group, the SL(4, R), or the GL(4-R) covering subgroup.

1,474 citations

Journal ArticleDOI
TL;DR: The present status of the quasi-local mass-energy-momentum and angular momentum constructions in general relativity is reviewed.
Abstract: The present status of the quasi-local mass-energy-momentum and angular momentum constructions in general relativity is reviewed. First the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities are recalled. Then the various specific constructions and their properties (both successes and defects) are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned. This review is based on the talks given at the Erwin Schrodinger Institute, Vienna, in July 1997, at the Universitat Tubingen, in May 1998, and at the National Center for Theoretical Sciences in Hsinchu and at the National Central University, Chungli, Taiwan, in July 2000.

395 citations

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TL;DR: In this article, a method was developed to extract the modified Einstein field equations in the limit of small metric fluctuations about the Minkowski vacuum, while allowing for the dynamics of the 20 independent coefficients for Lorentz violation.
Abstract: The pure-gravity sector of the minimal standard-model extension is studied in the limit of Riemann spacetime. A method is developed to extract the modified Einstein field equations in the limit of small metric fluctuations about the Minkowski vacuum, while allowing for the dynamics of the 20 independent coefficients for Lorentz violation. The linearized effective equations are solved to obtain the post-Newtonian metric. The corresponding post-Newtonian behavior of a perfect fluid is studied and applied to the gravitating many-body system. Illustrative examples of the methodology are provided using bumblebee models. The implications of the general theoretical results are studied for a variety of existing and proposed gravitational experiments, including lunar and satellite laser-ranging, laboratory experiments with gravimeters and torsion pendula, measurements of the spin precession of orbiting gyroscopes, timing studies of signals from binary pulsars, and the classic tests involving the perihelion precession and the time delay of light. For each type of experiment considered, estimates of the attainable sensitivities are provided. Numerous effects of local Lorentz violation can be studied in existing or near-future experiments at sensitivities ranging from parts in ${10}^{4}$ down to parts in ${10}^{15}$.

377 citations

Journal ArticleDOI
TL;DR: The present status of the quasi-local mass, energy-Momentum and angular-momentum constructions in general relativity is reviewed.
Abstract: The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities, are recalled. Then, the various specific constructions and their properties (both successes and deficiencies are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned.

354 citations