We consider a general stationary solution and derive the general laws for accretion of rotating perfect fluids. For non-degenerate and degenerate Fermi and Bose fluids we derive new effects that mimic the center-of-mass-energy effect of two colliding particle in the vicinity of horizons. Nondegenerate fluids see their chemical potential grow arbitrarily and ultra-relativistic Fermi fluids see their specific enthalpy and Fermi momentum grow arbitrarily too while the latter vanishes gradually for non-relativistic Fermi fluids. For degenerate Bose fluids two scenarios remain possible as the fluid approaches a horizon: a) The Bose-Einstein condensation ceases or b) the temperature drops gradually down to zero. The critical flow is also investigated.
I. WHAT IS ACCRETION?Given a metric solution of spacetime, a geodesic motion is the process by which a massive or massless test particle "falls" freely. The fall motion may be bounded (circular motion or else) or unbounded (scattering motion). The free fall of the test particle does not disturb, affect, or modify the given geometry: No back reaction effects are taken into consideration. Moreover, no group motion is treated in geodesic motion. Back reaction effects are present in the calculation of gravitational self forces where the motion of the "small" body is still seen as geodesic in the perturbed metric.Accretion is an advanced state of motion. It describes group motion with and without back reaction and it is generally non-geodesic. By group motion it is meant that the accreting matter is modeled by a fluid and that each fluid element encompasses a) a sufficiently large number of particles to be described statistically by an average pressure, average temperature, average particle number density, and average energy density; b) a sufficiently small number of particles compared to the whole system (accreting matter, atmosphere, etc). These conditions are easily met in astrophysics and atmospheric motion. The presence of a gradient of pressure, which is a sort of fluid group self force, renders the accretion motion non-geodesic.In accretion motion back reaction effects are taken into consideration in numerical and simulation analyses [1][2][3]. Full analytical treatments [4-8] drop back reaction effects for simplicity and cognitive treatments [9-15] may include emission effects and neglect back reaction too.All the above-mentioned treatments make common simplificative physical assumptions of symmetry concerning both the given background geometry and the fluid. They assume the background metric to remain stationary and time-independent during accretion [16]. The analysis remains valid for accretion time, larger than free-fall time, and much smaller than the ratio mass/(mass rate change) of the star.In this work we will keep using the standard set of simplificative assumptions to describe the accretion of rotating perfect fluids onto rotating black holes with no back reaction or emission effects. In Sec. II we present the accretion model and in sec. III we derive the gen...