Jeans mass for anisotropic matter

We extend the Jeans instability criterion to systems with anisotropic pressures (principal stresses unequal). We show that instabilities may develop for masses of several orders of magnitude smaller than the corresponding Jeans mass for an ideal locally isotropic gas. Also it shown that the fragmentation ensuing the onset of instabilities may terminate with fragment masses of the order of, or even smaller than, brown dwarfs instead of the solar mass as in the case for locally isotropic gas.