Abstract
It is shown that the equation of state μ=p for an ideal fluid follows from the condition of integrability of Einstein's equations for the metric ds2=R2T2dω2+e2λdr2−e2νdt2. In this case, the system of Einstein's equations turns out to be indeterminate and has an infinite number of solutions for R′ ≠ 0. These solutions describe fields with nonzero acceleration, expansion, and shear tensor of particles. The obtained solutions correct the results obtained by J. Hajj-Boutros, J. Math. Phys.,26, 771 (1985). The unique solution of Einstein's equations for the state μ=p of a fluid is obtained to within arbitrary constants for R′=0.
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Literature cited
L. D. Landau and E. M. Lifshitz, Field Theory [in Russian], Nauka, Moscow (1973).
J. Hajj-Boutros, J. Math. Phys.,26, 771–773 (1985).
V. I. Obozov, Deposited at VINITI, on May 12, 1985. Dep. No. 3218 (1985).
N. Van Den Bergh and P. Wiels, Gen. Relat. Gravit.,17, 223–243 (1983).
Additional information
Naval Engineering College, Novosibirsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 91–94, June, 1992.
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Obozov, V.I. A class of spherically symmetric ideal fluid fields. Russ Phys J 35, 565–568 (1992). https://doi.org/10.1007/BF00559184
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DOI: https://doi.org/10.1007/BF00559184