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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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/8/408 |
| _version_ | 1827617532189605888 |
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| author | Mohammad Salman Musavvir Ali Mohd Bilal |
| author_facet | Mohammad Salman Musavvir Ali Mohd Bilal |
| author_sort | Mohammad Salman |
| collection | DOAJ |
| 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mi>p</mi></mrow></semantics></math></inline-formula>-waves of Petrov type N if admit curvature inheritance symmetry, then conformal motion implies homothetic motion. |
| first_indexed | 2024-03-09T09:48:19Z |
| format | Article |
| id | doaj.art-e4d3cabd2db6414e802d7b736dae1fe0 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T09:48:19Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-e4d3cabd2db6414e802d7b736dae1fe02023-12-02T00:24:19ZengMDPI AGUniverse2218-19972022-08-018840810.3390/universe8080408Curvature Inheritance Symmetry in Ricci Flat SpacetimesMohammad Salman0Musavvir Ali1Mohd Bilal2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematical Sciences, Faculty of Applied Sciences, Umm Al Qura University, Makkah P.O. Box 21955, Saudi ArabiaIn 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mi>p</mi></mrow></semantics></math></inline-formula>-waves of Petrov type N if admit curvature inheritance symmetry, then conformal motion implies homothetic motion.https://www.mdpi.com/2218-1997/8/8/408curvature symmetry inheritanceRicci flat spacetimesgravitational wavesnull tetrad |
| spellingShingle | Mohammad Salman Musavvir Ali Mohd Bilal Curvature Inheritance Symmetry in Ricci Flat Spacetimes Universe curvature symmetry inheritance Ricci flat spacetimes gravitational waves null tetrad |
| title | Curvature Inheritance Symmetry in Ricci Flat Spacetimes |
| title_full | Curvature Inheritance Symmetry in Ricci Flat Spacetimes |
| title_fullStr | Curvature Inheritance Symmetry in Ricci Flat Spacetimes |
| title_full_unstemmed | Curvature Inheritance Symmetry in Ricci Flat Spacetimes |
| title_short | Curvature Inheritance Symmetry in Ricci Flat Spacetimes |
| title_sort | curvature inheritance symmetry in ricci flat spacetimes |
| topic | curvature symmetry inheritance Ricci flat spacetimes gravitational waves null tetrad |
| url | https://www.mdpi.com/2218-1997/8/8/408 |
| work_keys_str_mv | AT mohammadsalman curvatureinheritancesymmetryinricciflatspacetimes AT musavvirali curvatureinheritancesymmetryinricciflatspacetimes AT mohdbilal curvatureinheritancesymmetryinricciflatspacetimes |