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Curvature Inheritance Symmetry in Ricci Flat Spacetimes
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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.
Title: Curvature Inheritance Symmetry in Ricci Flat Spacetimes
Description:
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.
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