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Analysis and more General Solutions of Einstein Field Equation in f(R, T) Gravity

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Abstract

In this paper the major work is done on the optimal solution of f(R, T) gravity 00-component field equation. Explicit derivation of 00 and 11-components has been done. Optimal existence of solution of 00-component has been formulated using fixed point theory. The equivalence of 00-component of f(R, T) gravity field equation with wave equation having the source term has been explicitly proved. Also the computational more general solutions of 00-component of f(R, T) gravity field equation is explained in the various surface plot. Also the contour as well as 2D-pairs (f, R) and (f, T) have been examined and analyzed.

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Data availability

The solutions of Einstein field equations in modified gravity are discussed in the most general environment, specific data has been tested but the constant and the data availability has been cited at different stages if they are used somewhere.

Notes

  1. The action can be understood as a showcase of the dynamical and spatial propertise of the physical system and remains a key point to extract the various equations called the gravitational field equations. The total action of the system is equipped with the matter distribution which act as a source of gravitational field and the gravitational field itself see [16].

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Acknowledgements

This research project was supported by a grant from the “Research Center of the Female Scientific and Medical Colleges”, Deanship of Scientific Research, King Saud University. We pay our gratitude to Dr. Muhammad Ozair Ahmed, HOD, Mathematics and Statistics, The University of Lahore, lahore,Pakistan, for his contribution in the field of Numerical solution of PDEs and ODEs and also to Dr. Muhammad Sharif, Dean of Sciences, the University of Punjab, Lahore, Pakistan, for his long time servicing in the field of cosmology in Pakistan.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia

    Reem K. Alhefthi

  2. School of Foundation Studies and Mathematics, OUC with Liverpool john Moores University (UK), Qatar Campus, 12253, Doha, Qatar

    Muhammad Sajid Iqbal

  3. Department of Humanities & Basic Science, Military College of Signals, NUST, Islamabad, Pakistan

    Muhammad Sajid Iqbal

  4. Nust College of Electrical and Mechanical Engineering, Department of Basic Sciences and Humanities, NUST College of EME, Rawalpindi, Pakistan

    Saba Sohail

  5. Science Faculty, Department of Mathematics, Firat University, 23119, Elazig, Turkey

    Mustafa Inc

  6. China Medical University, Department of Medical Research, 40402, Taichung, Taiwan

    Mustafa Inc

Authors
  1. Reem K. Alhefthi
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  2. Muhammad Sajid Iqbal
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  3. Saba Sohail
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  4. Mustafa Inc
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Contributions

R.K.A., M.S.I. have contributed to the analysis and the equivalence result of the obtained Einstein field equations in the modified gravity further the contribution by S.S. and M.I. includes write-up, derivation of Einstein field equations in modified gravity, computation, simulation, and interpretation of results also S.S. has developed the solution bounds in abstract function spaces.

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Correspondence to Mustafa Inc.

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Alhefthi, R.K., Iqbal, M.S., Sohail, S. et al. Analysis and more General Solutions of Einstein Field Equation in f(R, T) Gravity. Int J Theor Phys 63, 24 (2024). https://doi.org/10.1007/s10773-024-05555-5

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