Counter-rotating relativistic static thin disks

Abstract

A detailed study of the Counter-Rotating Model (CRM) for generic fi-nite static axially symmetric thin disks with nonzero radial pressure is presented. We find a general constraint over the counter-rotating tan-gential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counter-rotating perfect fluids. We also found expressions for the energy density and pressure of the counter-rotating fluids. Then we shown that, in general, it is not possible to take the two counter-rotating fluids as circulating along geodesics neither take the two counter-rotating tangential velocities as equal and opposite. An specific example is studied where we obtain some CRM with well defined counter-rotating tangential velocities that are agree with the strong en­ergy condition, but there are regions of the disk with negative energy density, in violation of the weak energy condition.