Physical acceptability of isolated, static, spherically symmetric, perfectfluid solutions of Einstein's equations

We ask the following question: Of the exact solutions to Einstein's equatio ns extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The can didate solutions were subjected to the following elementary tests: (i) isot ropy of the pressure, (ii) regularity at the origin, (iii) positive definit eness of the energy density and pressure at the origin, (iv) vanishing of t he pressure at some finite radius, (v) monotonic decrease of the energy den sity and pressure with increasing radius, and (vi) subluminal sound speed. A total of 127 candidate solutions were found. Only 16 of these passed all the tests. Of these 16, only 9 have a sound speed which monotonically decre ases with radius. The analysis was facilitated by use of the computer algeb ra system GRTensorII. (C) 1998 Elsevier Science B.V.