A class of spherically symmetric ideal fluid fields

It is shown that the equation of state =p for an ideal fluid follows from the condition of integrability of Einstein's equations for the metric ds²=R²T²d²+e²dr²–e²dt². 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 =p of a fluid is obtained to within arbitrary constants for R=0.Naval Engineering College, Novosibirsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 91–94, June, 1992.