a maximum of energy. As one can easily see, the system will either expand or collapse depending on its actual baryon number compared to N$_{min}$ . Moreover, the electrostatic force can support only the surface layer of matter where the electric field is nonzero. The inner layers of the star require the kinetic pressure to resist gravity. Therefore, the mechanism discussed in ref. [7] cannot produce any new stable object. Inclusion of the electrostatic effects will only slightly increase the star mass, see e. g. ref. [8]. In conclusion, we have demonstrated that very strong electric fields can be generated on a sharp boundary separating the bulk matter from the vacuum. The strength of the field is determined by the separation of positive and negative charges in the surface layer. For the proton charge distribution with the diffuseness parameter of a nuclear scale the field strength may exceed significantly the critical value for the electron-positron pair production. The field strength diminishes when the charge distribution becomes more and more smooth. We have also considered star-like configurations with a strong electric field on the boundary. Our simple analysis shows that such electric field alone cannot balance the gravitational force to produce stable objects. The stable compact star configurations appear only when the counter-pressure of degenerate fermions is taken into consideration. For a more accurate description of compact stars with strong electric fields one should perform calculations within General Relativity and include effects of strong interactions in the energy of the nuclear core. We are grateful to Prof. Remo Ruffini who attracted our attention to the problems discussed in this paper. We acknowledge his kind hospitality during our visit to the Inter- national Center for Relativistic Astrophysics (ICRA) at Pescara in March 2009. We also thank Dr. Thomas B¨ urvenich and members of the ICRA group for fruitful discussions. This work was supported in part by the DFG Grant 436 RUS 113/957/0-1 (Germany), and by the Grants NS-3004.2008.2 and RFBR 09-02-91331 (Russia). 11 [1] A. Battachariya, I.N. Mishustin and W. Greiner, Deconfinement Phase Transition in Compact Stars: Maxwell vs Gibbs Constraction of the Mixed phase,J. Phys. G: Nucl. Part. Phys. 37 , 025201 (2010). [2] M. Dey, I. Bombaci, J. Dey, S. Ray and B.C. Samanta, Phys. Lett. B438 , 123 (1998); Phys. Lett. B467 , 303 (1999).