Curvature inheritance symmetry on M-projectively flat spacetimes

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Shaikh A. A., Ali M., Salman M., Zengin F.

International Journal of Geometric Methods in Modern Physics, vol.20, no.2, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1142/s0219887823500883
  • Journal Name: International Journal of Geometric Methods in Modern Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: conformal motion, curvature inheritance, Einstein field equations, flat spacetime, M-projective curvature tensor, perfect fluid spacetime
  • Istanbul Technical University Affiliated: Yes


© 2023 World Scientific Publishing Company.The paper aims to investigate curvature inheritance (CI) symmetry in M-projectively flat spacetimes. It is shown that the CI symmetry in M-projectively flat spacetime is a conformal motion. We have proved that M-projective curvature tensor follows the symmetry inheritance property along a vector field ζ, when spacetime admits the conditions of both CI symmetry and conformal motion or motion along the vector field ζ. Also, we have derived some results for M-projectively flat spacetime with perfect fluid following the Einstein field equations (EFEs) with a cosmological term and admitting the CI symmetry along the vector field ζ. We have shown that an M-projectively flat perfect fluid spacetime obeying the EFEs with a cosmological term and admitting the CI symmetry along a vector field ζ is either a vacuum or satisfies the vacuum-like equation of state. We have also shown that such spacetimes with the energy-momentum tensor of an electromagnetic field distribution do not admit any curvature symmetry of general relativity. Finally, an example of M-projectively flat spacetime has been exhibited.