Global solution for a viscous accretion disc around a rotating compact object: pseudo‐general‐relativistic study

We study the solution for a viscous accretion disc around a rotating compact/central object having a hard surface, i.e. a neutron star, a strange star or any other highly gravitating object. We choose a pseudo‐Newtonian approach to describe the relativistic accretion disc. For this purpose, a new pseudo‐Newtonian potential is established that is applicable to describing the relativistic properties of a star and its disc. As we know, the Hartle–Thorne metric can describe the geometry of a star as well as the space–time outside it, so we use this metric to establish our potential. Our potential reproduces the marginally stable orbit exactly as does general relativity. It also reproduces the marginally bound orbit and specific mechanical energy at the marginally stable orbit with at most 4 and 10 per cent error, respectively. Using this potential, we study the global parameter space of the accretion disc. Thus we find the physical parameter regime for which a stable accretion disc can be formed around a gravitating object with a hard surface. We also study how the fluid properties get changed with different rotations of the central star. We show that, with a change in rotation of the central object, the valid disc parameter region changes dramatically. We also show the effect of viscosity on the fluid properties of the disc. Subsequently, we give a theoretical prediction of kilohertz QPO frequencies, at least for one of a pair, for a fast‐rotating compact object such as 4U 1636‐53.