Stationary axially symmetric relativistic thin discs with nonzero radial pressure

A detailed analysis of the surface energy-momentum (SEMT) tensor of stationary axially symmetric relativistic thin discs with nonzero radial pressure is presented. The physical content of the SEMT is analysed and expressions for the velocity vector, energy density, principal stresses and heat flow are obtained. We also present the counter-rotating model interpretation for these discs by considering the SEMT as the superposition of two counter-rotating perfect fluids. We analyse the possibility of counter-rotation along geodesics as well as counter-rotation with equal and opposite tangential velocities, and explicit expressions for the velocities are obtained in both the cases. By assuming a given choice for the counter-rotating velocities, explicit expressions for the energy densities and pressures of the counter-rotating fluids are then obtained. Some simple thin disc models obtained from the Kerr solution are also presented.