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Submillimeter corrections to gravity and the metastability of white dwarf and neutron stars

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.