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The importance of general relativity to the induced electric field exteriorto pulsars has been investigated by assuming aligned vacuum and non-vacuummagnetosphere models. For this purpose the stationary and axisymmetric vectorpotential in Schwarzschild geometry has been considered and the correspondingexpressions for the induced electric field due to the rotation of the magneticdipole have been derived for both vacuum and non-vacuum conditions. Due to thechange in the magnetic dipole field in curved spacetime the induced electricfield also changes its magnitude and direction and increases significantly nearthe surface of the star. As a consequence the surface charge density, theacceleration of charged particles in vacuum magnetospheres and the space chargedensity in non-vacuum magnetosphere greatly increase near the surface of thestar. The results provide the most general feature of the important role playedby gravitation and could have several potentially important implications forthe production of high-energy radiation from pulsars.Comment: 16 pages, LATEX, 7 figures available upon request, to appear in The  Astrophysical Journa

General Relativistic Effects on the Induced Electric Field Exterior to Pulsars