Abstract
The Einstein field equations for an irrotational perfect fluid with pressurep, equal to energy density are studied when the space-time is conformally flat. The coordinate transformation to co-moving coordinates is discussed. The energy and Hawking-Penrose inequalities are studied. Static and non-static solutions of the field equations are obtained. It is interesting to note that in the static case the only spherically-symmetric conformally flat solution for self-gravitating fluid is simply the empty flat space-time of general relativity.
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References
Banerjee, A. and Santos, N. D.: 1981,J. Math. Phys. 22, 1075.
Hawking, S. W. and Penrose, R.: 1970,Proc. Roy. Soc. A314, 529.
Letelier, P. S.: 1975,J. Math. Phys. 16, 1488.
Letelier, P. S.: 1979,J. Math. Phys. 20, 2078.
Letelier, P. S. and Tabensky, R. R.: 1975,Nuovo Cimento 28B, 407.
Rao, V. U. M. and Reddy, D. R. K.: 1982,Gen. Rel. Grav. 14, 1017.
Ray, D.: 1976,J. Math. Phys. 17, 1171.
Reddy, D. R. K.: 1979,J. Math. Phys. 20, 23.
Reddy, D. R. K. and Iannaiah, P.: 1985,Ind. J. Pure Appl. Phys. 23, 450.
Singh, T. and Yadav, R. B. S.: 1978,Ind. J. Pure Appl. Math. 9, 900.
Tabensky, R. and Taub, A. H.: 1973,Comm. Math. Phys. 29, 61.
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Reddy, D.R.K. Self-gravitating fluid in a conformally-flat space-time. Astrophys Space Sci 138, 121–125 (1987). https://doi.org/10.1007/BF00642870
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DOI: https://doi.org/10.1007/BF00642870