Junction conditions and static fluid cylinders in Lyra's geometry

Junction conditions for Sen's theory in Lyra's geometry are considered. It is proposed that for any gauge function the standard O'Brien-Synge and Lichnerowicz junction conditions should be supplemented by demanding continuity of the displacement vector across the interface. A class of internal solutions of the Sen equations with a source term given by the energy-momentum tensor of a one-component perfect fluid with the ultrarelativistic equation of state that is expressible in terms of Bessel functions is proposed. The internal solution is regularly matched by means of the junction conditions to the exterior solution. The resulting two-parameter solution is globally non-Euclidean.