# Elucidation of covariant proofs in general relativity: example of the use of algebraic software in the shear-free conjecture in MAPLE

Elucidation of covariant proofs in general relativity: example of the use of algebraic software... In this paper we explore the use of a new algebraic software package in providing independent covariant proof of a conjecture in general relativity. We examine the proof of two sub-cases of the shear-free conjecture $$\displaystyle \sigma =0 {\displaystyle \, =>}\, {\displaystyle \omega }\,{\displaystyle \varTheta } =0$$ σ = 0 = > ω Θ = 0 by Senovilla et al. (Gen. Relativ. Gravit 30:389–411, 1998): case 1: for dust; case 2: for acceleration parallel to vorticity. We use TensorPack, a software package recently released for the Maple environment. In this paper, we briefly summarise the key features of the software and then demonstrate its use by providing and discussing examples of independent proofs of the paper in question. A full set of our completed proofs is available online at http://www.bach2roq.com/science/maths/GR/ShearFreeProofs.html . We are in agreeance with the equations provided in the original paper, noting that the proofs often require many steps. Furthermore, in our proofs we provide fully worked algebraic steps in such a way that the proofs can be examined systematically, and avoiding hand calculation. It is hoped that the elucidated proofs may be of use to other researchers in verifying the algebraic consistency of the expressions in the paper in question, as well as related literature. Furthermore we suggest that the appropriate use of algebraic software in covariant formalism could be useful for developing research and teaching in GR theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png General Relativity and Gravitation Springer Journals

# Elucidation of covariant proofs in general relativity: example of the use of algebraic software in the shear-free conjecture in MAPLE

, Volume 50 (1) – Dec 2, 2017
23 pages

/lp/springer_journal/elucidation-of-covariant-proofs-in-general-relativity-example-of-the-IHbbmnZFV2
Publisher
Springer US
Subject
Physics; Theoretical, Mathematical and Computational Physics; Classical and Quantum Gravitation, Relativity Theory; Differential Geometry; Astronomy, Astrophysics and Cosmology; Quantum Physics
ISSN
0001-7701
eISSN
1572-9532
D.O.I.
10.1007/s10714-017-2325-5
Publisher site
See Article on Publisher Site

### Abstract

In this paper we explore the use of a new algebraic software package in providing independent covariant proof of a conjecture in general relativity. We examine the proof of two sub-cases of the shear-free conjecture $$\displaystyle \sigma =0 {\displaystyle \, =>}\, {\displaystyle \omega }\,{\displaystyle \varTheta } =0$$ σ = 0 = > ω Θ = 0 by Senovilla et al. (Gen. Relativ. Gravit 30:389–411, 1998): case 1: for dust; case 2: for acceleration parallel to vorticity. We use TensorPack, a software package recently released for the Maple environment. In this paper, we briefly summarise the key features of the software and then demonstrate its use by providing and discussing examples of independent proofs of the paper in question. A full set of our completed proofs is available online at http://www.bach2roq.com/science/maths/GR/ShearFreeProofs.html . We are in agreeance with the equations provided in the original paper, noting that the proofs often require many steps. Furthermore, in our proofs we provide fully worked algebraic steps in such a way that the proofs can be examined systematically, and avoiding hand calculation. It is hoped that the elucidated proofs may be of use to other researchers in verifying the algebraic consistency of the expressions in the paper in question, as well as related literature. Furthermore we suggest that the appropriate use of algebraic software in covariant formalism could be useful for developing research and teaching in GR theory.

### Journal

General Relativity and GravitationSpringer Journals

Published: Dec 2, 2017

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations