Research Article
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Spacetimes and Almost Ricci-Yamabe Solitons

Year 2025, Volume: 18 Issue: 1, 143 - 150, 24.04.2025

Ansari Rakesh Baidya , U.c. De , Krishnendu De

Abstract

This article investigates almost Ricci-Yamabe solitons and gradient almost Ricci-Yamabe solitons in spacetimes. Initially, we demonstrate that if a spacetime allows an almost Ricci-Yamabe soliton with a conformal vector field as potential vector field, then the spacetime turns into an Einstein spacetime. Next, we examine that if a spacetime admits an almost Ricci-Yamabe soliton with a recurrent vector field as potential vector field, then the spacetime becomes perfect fluid spacetime. Then, it is shown that if a generalized Robertson-Walker spacetime admits an almost Ricci-Yamabe soliton or a gradient almost Ricci-Yamabe soliton, then it represents a perfect fluid spacetime. Consequently, we derive a number of interesting corollaries. We conclude providing an example of an almost Ricci-Yamabe solitons.

Keywords

Perfect fluid spacetimes generalized Robertson-Walker spacetimes almost Ricci-Yamabe solitons

References

  • Alias, L., Romero, A., Sanchez, M.: Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes. Gen. Relat. Gravit. 27, 71-84 (1995).
  • Blaga, A. M.: Solitons and geometrical structures in a perfect fluid spacetime. Rocky Mountain J. Math. 50, 41–53 (2020).
  • Chen, B. Y.: A simple characterization of generalized Robertson-Walker spacetimes. Gen. Relativ. Gravit. 46, 1833 (2014).
  • Chen, B.Y., Deshmukh S.: Yamabe and Quasi-Yamabe Solitons on Euclidean Submanifolds. Mediter. J. Math. 15, 1-9 (2018).
  • De, U. C., Gezer, A.: A short note on generalized Robertson Walker spacetimes . Turk. J. Math. 48, 955-964 (2024).
  • De, K., Khan, M. N. I., De, U. C.: Characterization of generalized Robertson-Walker spacetimes concerning gradient solitons. Heliyon 10 (4), e25702 (2024). https://doi.org/10.1016/j.heliyon.2024.e25702
  • De, K., De, U.C.: Investigation on gradient solitons in perfect fluid spacetimes. Reports on Math. Phys. 91, 277-289 (2023).
  • De, K., De, U.C.: Ricci-Yamabe solitons in f(R)-gravity. Int. Electron. J. Geom. 16(1), 334-342 (2023).
  • De, U. C., Mantica, C. A. and Suh,Y.J.: Perfect fluid spacetimes and gradient solitons . Filomat 36, 529-842 (2022).
  • De, U. C., Sardar, A.: Static perfect fluid spacetimes on GRW spacetimes, Anal. Math. Phys. 13, 44 (2023).
  • Fialkow, A.: Conformal geodesics. Trans. Amer. Math. Soc. 45, 443-473 (1939).
  • Gutierrez, M., Olea, B.: Global decomposition of a Lorentzian manifold as a generalized Robertson-Walker space. Differ. Geom. Appl. 27, 146-156, (2009).
  • Guler, S., Crasmareanu, M.: Ricci-Yamabe maps for Riemannian flow and their volume variation and volume entropy. Turk. J. Math. 43, 2631-2641, (2019).
  • Hervik, S., Ortaggio, M., Wylleman, L.: Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension. Class. Quantum Grav. 30, 165014 (2013).
  • Mantica C. A., Molinari, L. G.: Generalized Robertson-Walker spacetimes-A survey. Int. J. Geom. Methods Mod. Phys. 14, 1730001 (2017).
  • Mantica, C. A., Molinari, L. G.: On the Weyl and the Ricci tensors of generalized Robertson–Walker spacetimes. J. Math. Phys. 57, 102502 (2016).
  • Mantica, C. A., De, U. C., Suh, Y. J., Molinari, L. G.: Perfect fluid spacetimes with harmonic generalized curvature tensor. Osaka J. Math. 56,173-182 (2019).
  • Siddiqi, M. D., De, U. C.: Relativistic perfect fluid spacetimes and Ricci-Yamabe solitons . Lett. Math. Phys. 112 (2022).
  • Singh, J. P., Khatri, M.: On Ricci-Yamabe solitons and geometrical structure in a perfect fluid spacetime. Africa Mathematica 32, 1645-1656 (2021).
  • Sharma, R.: Conformal vector fields in symmetric and conformal symmetric spaces . Int J. Math. Sci. 12, 85-88 (1989).
  • Sharma, R.: Proper conformal symmetries of spacetimes with divergence-free Weyl tensor . J. Math. Phys. 34, 3582-3587 (1993).
  • Stephani, H., Kramer, D., Mac-Callum, M., Hoenselaers, C., Herlt, E.: Exact Solutions of Einstein’s Field Equations. Cambridge University Press, Cambridge (2009).
  • Yano, K.: On torse forming direction in a Riemannian space. Proc. Imp. Acad. Tokyo 20, 340-345 (1944).

Year 2025, Volume: 18 Issue: 1, 143 - 150, 24.04.2025

Ansari Rakesh Baidya , U.c. De , Krishnendu De

Abstract

References

  • Alias, L., Romero, A., Sanchez, M.: Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes. Gen. Relat. Gravit. 27, 71-84 (1995).
  • Blaga, A. M.: Solitons and geometrical structures in a perfect fluid spacetime. Rocky Mountain J. Math. 50, 41–53 (2020).
  • Chen, B. Y.: A simple characterization of generalized Robertson-Walker spacetimes. Gen. Relativ. Gravit. 46, 1833 (2014).
  • Chen, B.Y., Deshmukh S.: Yamabe and Quasi-Yamabe Solitons on Euclidean Submanifolds. Mediter. J. Math. 15, 1-9 (2018).
  • De, U. C., Gezer, A.: A short note on generalized Robertson Walker spacetimes . Turk. J. Math. 48, 955-964 (2024).
  • De, K., Khan, M. N. I., De, U. C.: Characterization of generalized Robertson-Walker spacetimes concerning gradient solitons. Heliyon 10 (4), e25702 (2024). https://doi.org/10.1016/j.heliyon.2024.e25702
  • De, K., De, U.C.: Investigation on gradient solitons in perfect fluid spacetimes. Reports on Math. Phys. 91, 277-289 (2023).
  • De, K., De, U.C.: Ricci-Yamabe solitons in f(R)-gravity. Int. Electron. J. Geom. 16(1), 334-342 (2023).
  • De, U. C., Mantica, C. A. and Suh,Y.J.: Perfect fluid spacetimes and gradient solitons . Filomat 36, 529-842 (2022).
  • De, U. C., Sardar, A.: Static perfect fluid spacetimes on GRW spacetimes, Anal. Math. Phys. 13, 44 (2023).
  • Fialkow, A.: Conformal geodesics. Trans. Amer. Math. Soc. 45, 443-473 (1939).
  • Gutierrez, M., Olea, B.: Global decomposition of a Lorentzian manifold as a generalized Robertson-Walker space. Differ. Geom. Appl. 27, 146-156, (2009).
  • Guler, S., Crasmareanu, M.: Ricci-Yamabe maps for Riemannian flow and their volume variation and volume entropy. Turk. J. Math. 43, 2631-2641, (2019).
  • Hervik, S., Ortaggio, M., Wylleman, L.: Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension. Class. Quantum Grav. 30, 165014 (2013).
  • Mantica C. A., Molinari, L. G.: Generalized Robertson-Walker spacetimes-A survey. Int. J. Geom. Methods Mod. Phys. 14, 1730001 (2017).
  • Mantica, C. A., Molinari, L. G.: On the Weyl and the Ricci tensors of generalized Robertson–Walker spacetimes. J. Math. Phys. 57, 102502 (2016).
  • Mantica, C. A., De, U. C., Suh, Y. J., Molinari, L. G.: Perfect fluid spacetimes with harmonic generalized curvature tensor. Osaka J. Math. 56,173-182 (2019).
  • Siddiqi, M. D., De, U. C.: Relativistic perfect fluid spacetimes and Ricci-Yamabe solitons . Lett. Math. Phys. 112 (2022).
  • Singh, J. P., Khatri, M.: On Ricci-Yamabe solitons and geometrical structure in a perfect fluid spacetime. Africa Mathematica 32, 1645-1656 (2021).
  • Sharma, R.: Conformal vector fields in symmetric and conformal symmetric spaces . Int J. Math. Sci. 12, 85-88 (1989).
  • Sharma, R.: Proper conformal symmetries of spacetimes with divergence-free Weyl tensor . J. Math. Phys. 34, 3582-3587 (1993).
  • Stephani, H., Kramer, D., Mac-Callum, M., Hoenselaers, C., Herlt, E.: Exact Solutions of Einstein’s Field Equations. Cambridge University Press, Cambridge (2009).
  • Yano, K.: On torse forming direction in a Riemannian space. Proc. Imp. Acad. Tokyo 20, 340-345 (1944).
There are 23 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Ansari Rakesh Baidya 0009-0008-4057-0493

U.c. De 0000-0002-8990-4609

Krishnendu De 0000-0001-6520-4520

Early Pub Date April 20, 2025
Publication Date April 24, 2025
Submission Date December 17, 2024
Acceptance Date February 5, 2025
Published in Issue Year 2025 Volume: 18 Issue: 1

Cite

APA Baidya, A. R., De, U., & De, K. (2025). Spacetimes and Almost Ricci-Yamabe Solitons. International Electronic Journal of Geometry, 18(1), 143-150.
AMA Baidya AR, De U, De K. Spacetimes and Almost Ricci-Yamabe Solitons. Int. Electron. J. Geom. April 2025;18(1):143-150.
Chicago Baidya, Ansari Rakesh, U.c. De, and Krishnendu De. “Spacetimes and Almost Ricci-Yamabe Solitons”. International Electronic Journal of Geometry 18, no. 1 (April 2025): 143-50.
EndNote Baidya AR, De U, De K (April 1, 2025) Spacetimes and Almost Ricci-Yamabe Solitons. International Electronic Journal of Geometry 18 1 143–150.
IEEE A. R. Baidya, U. De, and K. De, “Spacetimes and Almost Ricci-Yamabe Solitons”, Int. Electron. J. Geom., vol. 18, no. 1, pp. 143–150, 2025.
ISNAD Baidya, Ansari Rakesh et al. “Spacetimes and Almost Ricci-Yamabe Solitons”. International Electronic Journal of Geometry 18/1 (April 2025), 143-150.
JAMA Baidya AR, De U, De K. Spacetimes and Almost Ricci-Yamabe Solitons. Int. Electron. J. Geom. 2025;18:143–150.
MLA Baidya, Ansari Rakesh et al. “Spacetimes and Almost Ricci-Yamabe Solitons”. International Electronic Journal of Geometry, vol. 18, no. 1, 2025, pp. 143-50.
Vancouver Baidya AR, De U, De K. Spacetimes and Almost Ricci-Yamabe Solitons. Int. Electron. J. Geom. 2025;18(1):143-50.
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