Static spheres are studied to investigate the link between the surface value of the potential (and therefore the observable redshift) and the highest occurring ratio of the trace of the pressure tensor to the local density. The transverse pressure is permitted to differ from the radial one. Both Newtonian and relativistic models are examined. Considerably larger redshift values are found when anisotropic pressures are allowed than in the isotropic case.
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Hermann Bondi (1992) studied this question.