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Algebraic invariants of the Riemann tensor in a four‐dimensional Lorentzian space

John Carminati, +1 more
- 01 Nov 1991 - 
- Vol. 32, Iss: 11, pp 3135-3140
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TLDR
In this paper, a set of 16 scalar invariants of the Riemann tensor is given, which is shown to contain complete minimal sets in the Einstein-Maxwell and perfect fluid cases.
Abstract: 
A set of 16 scalar invariants is given of the Riemann tensor which is shown to contain complete minimal sets in the Einstein–Maxwell and perfect fluid cases. All previously known sets fail to be complete in the perfect fluid case.

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Testing general relativity in cosmology

Mustapha Ishak
- 01 Jan 2019 - 
TL;DR: The review aims at providing an overall picture of the subject and an entry point to students and researchers interested in joining the field and a quick reference to recent results and constraints on testing gravity at cosmological scales.
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Alignment and algebraically special tensors in lorentzian geometry

Robert Milson, +3 more
- 01 Feb 2005 - 
TL;DR: In this paper, a dimension-independent theory of alignment in Lorentzian geometry is developed and applied to the tensor classification problem for the Weyl and Ricci tensors.
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Testing General Relativity in Cosmology

Mustapha Ishak
- 26 Jun 2018 - 
TL;DR: A review of recent developments and results in testing general relativity (GR) at cosmological scales is presented in this paper, where the authors provide an overall picture of the subject and an entry point to students and researchers interested in joining the field.
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Second order scalar invariants of the riemann tensor: applications to black hole spacetimes

Christian Cherubini, +4 more
- 01 Jul 2002 - 
TL;DR: In this article, the Kretschmann, Chern-Pontryagin and Euler invariants among the second order scalar invariants of the Riemann tensor in any spacetime in the Newman-Penrose formalism and in the framework of gravitoelectromagnetism are discussed.
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An effective formalism for testing extensions to General Relativity with gravitational waves

Solomon Endlich, +3 more
- 05 Apr 2017 - 
TL;DR: In this article, an Effective Field Theory (EFT) was proposed for the detection of gravitational waves from merging black holes, which is consistent with other experiments, including short distance tests of GR.
References
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Journal ArticleDOI

A review of the geometrical equivalence of metrics in general relativity

Anders Karlhede
- 01 Sep 1980 - 
TL;DR: In this article, a generalized Petrov classification is proposed to automatically give the dimensions of the isometry group and its isotropy subgroup, which can be used to obtain a coordinate-invariant description of a geometry.
Journal ArticleDOI

A tutorial introduction to Maple

Bruce W. Char, +4 more
- 01 Jun 1986 - 
TL;DR: The Maple computer algebra system is described and the user syntax and the mathematical power of the system for performing arithmetic, factoring, simplification, differentiation, integration, summation, solving algebraic equations, solving differential equations, series expansions, and matrix manipulations are shown.
Journal ArticleDOI

Invariants of General Relativity and the Classification of Spaces

Louis Witten
- 01 Jan 1959 - 
TL;DR: In this paper, a unique equivalence between the Riemann curvature tensor and two spinors is established, and fourteen invariants which can be constructed from the curvatures tensor are listed in terms of the spinors.
Journal ArticleDOI

Algebraic computing and the Newman-Penrose formalism in general relativity

S. J. Campbell, +1 more
- 01 Dec 1977 - 
TL;DR: A computer program is described, written in the symbolic manipulation language CAMAL, which performs this calculation of the curvature tensor of space-time, using the Newman-Penrose equations.
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Computer-aided classification of the Ricci tensor in general relativity

G. C. Joly, +1 more
- 01 Apr 1990 - 
TL;DR: In this article, a geometric interpretation of the Ricci tensor in general relativity is presented, and methods for distinguishing the sub-cases not separated by the multiplicities mentioned, and the resulting computer program described.
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Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "On the algebraic invariants of the four-dimensional riemann tensor" ?

Recently, Sneddon ( 1986 ) discussed briefly the form in which several authors have presented the fourteen independent algebraic invariants ( Haskins 1902 ) $ of the Riemann curvature tensor in four dimensions. Among the authors mentioned were GChCniau and Debever ( 1956a, b, c ) with implied priority of publication. The fourteen scalars according to Narlikar and Karmarkar are constructed from the following tensors. In this paper is determined the number of algebraic invariants as a function of the dimension of the space.