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We propose a four-neutrino model which can reconcile the existing data comingfrom underground experiments in terms of neutrino oscillations, together withthe hint from the LSND experiment and a possible neutrino contribution to thehot dark matter of the Universe. It applies the idea that extra compactdimensions, probed only by gravity and possibly gauge-singlet fields, can lowerthe fundamental scales such as the Planck, string or unification scales. Ourfourth light neutrino $\nu_s$ ($s$ for sterile) is identified with the zeromode of the Kaluza-Klein states. To first approximation \nu_sterile combineswith the nu_mu in order to form a Dirac neutrino with mass in the eV rangeleaving the other two neutrinos massless. The smallness of this mass scale(suitable for LSND and Hot Dark Matter) arises without appealing neither to asee-saw mechanism nor to a radiative mechanism, but from the volume factorassociated with the canonical normalization of the wave-function of the bulkfield in the compactified dimensions. % On the other hand the splitting between\nm and \nu_sterile (atmospheric scale) as well as the mass of the two otherneutrinos (solar mass scale) arise from the violation of the fermion number ondistant branes. We also discuss alternative scenarios involvingflavour-changing interactions. In one of them \ne can be in the electron-voltrange and therefore be probed in beta decay studies.Comment: 12 pages, latex, no figures, title changed, final version to be  published in Phys Rev

Light sterile neutrino from extra dimensions and four-neutrino solutions to neutrino anomalies