Curvature Inheritance Symmetry in Ricci Flat Spacetimes

In this article, we study curvature inheritance symmetry in Ricci flat spacetimes. We show that, if Ricci flat spacetimes are not of Petrov type N, and admit curvature inheritance symmetries, then the only existing symmetries are conformal motions. We also prove that the only Ricci flat spacetime th...

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Bibliographic Details
Published in:Universe (Basel) 2022-08, Vol.8 (8), p.408
Main Authors: Salman, Mohammad, Ali, Musavvir, Bilal, Mohd
Format: Article
Language:English
Subjects:
curvature symmetry inheritance
gravitational waves
Gravity
Inheritances
null tetrad
Partial differential equations
Ricci flat spacetimes
Space and time
Spacetime
Symmetry
Theory of relativity
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Summary:In this article, we study curvature inheritance symmetry in Ricci flat spacetimes. We show that, if Ricci flat spacetimes are not of Petrov type N, and admit curvature inheritance symmetries, then the only existing symmetries are conformal motions. We also prove that the only Ricci flat spacetime that admits a proper curvature inheritance symmetry and is of Petrov type other than N is the flat spacetime. Next, we find that the vacuum pp-waves of Petrov type N if admit curvature inheritance symmetry, then conformal motion implies homothetic motion.
ISSN:2218-1997
2218-1997
DOI:10.3390/universe8080408