An explicit necessary condition for the internal trapping of null geodesics , along with the occurrence of resonance scattering of axial gravitational waves , is proposed for static spherically symmetric perfect fluid solutions of Einstein ’ s equations .
Some exact inhomogeneous solutions which exhibit this trapping are given with special attention to boundary conditions and the physical acceptability of the space times .
In terms of the tenuity ( \alpha = R / M at the boundary ) all the examples given here lie in the narrow range 2.8 < \alpha < 2.9 .
The tenuity can be raised to more interesting values by the addition of an envelope without altering the trapping .