  The string inspired higher dimensional theories suggest modification of
Newton's law at submillimeter length scales. Inter-particle distances in white
dwarf and neutron stars are $10^{-10} cms$ and $10^{-13} cms$ respectively, and
therefore, the effects of of short distance corrections to gravity deserve
investigation. We show, by carrying out explicit analytical many-body
calculations that, in the presence of corrections, the normal state of these
compact stars become metastable. The actual quantum mechanical ground state of
the stars turns out to be unstable. However, the tunneling probability to the
unstable ground state is so small that the stars may remain trapped in the
metastable state practically for ever.
