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Solutions to the field equations and the deceleration parameter

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Abstract

We utilise a form for the Hubble parameter to generate a number of solutions to the Einstein field equations with variable cosmological constant and variable gravitational constant. The Hubble law utilised yields a constant value for the deceleration parameter. A variety of solutions is presented in the Robertson-Walker spacetimes. A generalisation of the cosmic scale factor is utilised in the anisotropic Bianchi I spacetime to illustrate that new solutions may also be found in spacetimes with less symmetry than Robertson-Walker. We also show that the constant deceleration parameter used is consistent with alternate theories of gravity by considering the scalar-tensor theory of Lau and Prokhovnik with ak = 0 Robertson-Walker background.

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References

  1. Abdel-Rahman A-M, M.: 1990,Gen. Rel. Grav. 22, 655.

  2. Beesham, A.: 1993, Preprint, (University of Zululand).

  3. Berman, M.S.: 1983,Nuovo Cimento 74B, 182.

  4. Berman, M.S.: 1990,Int. J. Theor. Phys. 29, 567.

  5. Berman, M.S.: 1991,Gen. Rel. Grav. 23, 465.

  6. Berman, M.S. and Gomide, F.M.: 1988,Gen. Rel. Grav. 20, 191.

  7. Berman, M.S. and Som, M.M.: 1990,Int. J. Theor. Phys. 29, 1411.

  8. Berman, M.S., Som, M.M., and Gomide, F.M.: 1989,Gen. Rel. Grav. 21, 287.

  9. Bertolami, O.: 1986a,Nuovo Cimento 93B, 36.

  10. Bertolami, O.: 1986b,Fortschr. Phys. 34, 829.

  11. Chow, T.L.: 1981,Lett. Nuovo Cimento 31, 119.

  12. Dirac, P.A.M.: 1938,Proc. R. Soc. London 165A, 199.

  13. Dirac, P.A.M.: 1979,Proc. R. Soc. London 365A, 19.

  14. Grøn, Ø.: 1986,Amer. J. Phys. 54, 46.

  15. Hellings, R.W.et al.: 1983,Phys. Rev. Lett. 51, 1609.

  16. Kramer, D.et al.: 1980,Exact Solutions of Einstein's Field Equations, Cambridge University Press, Cambridge.

  17. Lau, Y.K.: 1985,Austr. J. Phys. 38, 547.

  18. Lau, Y.K. and Prokhovnik, S.J.: 1986,Aust. J. Phys. 39, 339.

  19. Levitt, L.S.: 1980,Lett. Nuovo Cimento 29, 23.

  20. Maharaj, S.D. and Beesham, A.: 1988,J. Astrophys. Astr. 9, 67.

  21. Milne, E.A.: 1935,Relativity, Gravitation and World Structure, Oxford University Press, Oxford.

  22. Misner, C.W., Thorne, K.S., and Wheeler, J.A.: 1973,Gravitation, Freeman, San Francisco.

  23. Rowan-Robinson, M.: 1981,Cosmology, Oxford University Press, Oxford.

  24. Shapiro, I.I.et al.: 1971,Phys. Rev. Lett. 26, 27.

  25. Stephani, H.: 1990,General Relativity: An Introduction to the Theory of the Gravitational Field, Cambridge University Press, Cambridge.

  26. Van Flandern, T.C.: 1981,Astrophys. J. 248, 813.

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Maharaj, S.D., Naidoo, R. Solutions to the field equations and the deceleration parameter. Astrophys Space Sci 208, 261–276 (1993). https://doi.org/10.1007/BF00657941

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Keywords

  • Field Equation
  • Hubble Parameter
  • Alternate Theory
  • Deceleration Parameter
  • Gravitational Constant