  We ask the following question: Of the exact solutions to Einstein's equations
extant in the literature, how many could represent the field associated with an
isolated static spherically symmetric perfect fluid source? The candidate
solutions were subjected to the following elementary tests: i) isotropy of the
pressure, ii) regularity at the origin, iii) positive definiteness of the
energy density and pressure at the origin, iv) vanishing of the pressure at
some finite radius, v) monotonic decrease of the energy density 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 decreases with radius. The
analysis was facilitated by use of the computer algebra system GRTensorII.
