Sterile neutrinos are studied as subdominant contribution to solar neutrino physics. The mirror-matter neutrinos are considered as sterile neutrinos. We use the symmetric mirror model with gravitational communication between mirror and visible sectors. This communication term provides mixing between visible and mirror neutrinos with the basic scale mu=v^2/M_Pl=5*10^-6 eV, where v=174 GeV is the vacuum expectation value of the standard electroweak group and M_Pl is the Planckian mass. It is demonstrated that each mass eigenstate of active neutrinos splits into two states separated by small Delta m^2. Unsuppressed oscillations between active and sterile neutrinos nu_a --> nu_s occur only in transitions between each of these close pairs (``windows''). These oscillations are characterized by very small Delta m^2 and can suppress the flux and distort spectrum of pp-neutrinos in detectable way. The other observable effect is anomalous seasonal variation of neutrino flux, which appears in LMA solution. The considered subdominant neutrino oscillations nu_a <--> nu_s can reveal itself as big effects in observations of supernova neutrinos and high energy (HE) neutrinos. In the case of HE neutrinos they can provide a very large diffuse flux of active neutrinos unconstrained by the e-m cascade upper limit.Comment: 30 pags, 5 figs. V2: Refs added, minor editing. Accepted in NP

We consider non-renormalizable 1/M X interaction terms as a perturbation of the conventional neutrino mass matrix. Particular attention is given to the gravitational interaction with M X = M Pl . We find that for the degenerate neutrino mass spectrum, the considered perturbation generates a non-zero U e3 which is within reach of the high performance neutrino factories and just on the borderline to be of interest for supernova physics. For the hierarchical mass spectrum this effect is small. For 1/M X interaction terms with M X about the GUT scale, a detectable U e3 term is induced for the hierarchical mass spectra also. Numerical estimates are given for all the above mentioned cases and renormalization effects are considered.

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