Many-body treatment of white dwarf and neutron stars on the brane

Abstract

Brane-world models suggest modification of Newton's law of gravity on the 3-brane at submillimeter scales. The brane-world induced corrections are in higher powers of inverse distance and appear as additional terms with the Newtonian potential. The average interparticle distance in white dwarf and neutron stars is ${10}^{\ensuremath{-}10}\text{ }\text{ }\mathrm{cms}$ and ${10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{cms}$, respectively, and therefore, the effect of submillimeter corrections needs to be investigated. We show, by carrying out simple many-body calculations, that the mass and mass-radius relationship of the white dwarf and neutron stars are not effected by submillimeter corrections. However, our analysis shows that the correction terms in the effective theory give rise to force akin to surface tension in normal liquids.