Strong electric fields induced on a sharp stellar boundary 2 The Kurchatov Institute, Russian Research Center, 123182 Moscow, Russia (Dated: November 2, 2018) Igor N. Mishustin 1 , $^{2}$, Claudio Ebel$^{1}$, and Walter Greiner1 Due to a first order phase transition, a compact star may have a discontinuous distribution of baryon as well as electric charge densities, as e.g. at the surface of a strange quark star. The induced separation of positive and negative charges may lead to generation of supercritical electric fields in the vicinity of such a discontinuity. We study this effect within a relativistic Thomas- Fermi approximation and demonstrate that the strength of the electric field depends strongly on the degree of sharpness of the surface. The influence of strong electric fields on the stability of compact stars is discussed. It is demonstrated that stable configurations appear only when the counter-pressure of degenerate fermions is taken into consideration. PACS numbers: 97.60.-s, 12.38.Mh, 04.70-s 1 arXiv:1002.2541v1 [astro-ph.SR] 12 Feb 2010 Abstract $^{1}$Frankfurt Institute for Advanced Studies, J.W. Goethe University, D–60438 Frankfurt am Main, Germany