Relativistic Non-ideal flows

The problem of stationary, spherically symmetric accretion onto a Schwarzschild black hole is discussed here with the use of a formalism which is completely consistent with Einstein's General theory of Relativity. The transfer of heat is a significant part of this process, however treating it without approximations has proven difficult. Here I explore the adiabatic case first; then I consider a more general case by assuming that all the heat transfer happens through electromagnetic radiation. For the latter I apply the PSTF formalism which, roughly speaking, while still being relativistic allows for the decomposition of the radiation into its first moments: energy density and flux. The numerical analysis of the differential equations the problem can be reduced to shows a bimodal behaviour: a branch of solutions has a much higher efficiency (ratio of luminosity to accretion rate) than another. In order to treat this problem, first I briefly recall the formalism of general relativity; then I treat the basics of the relativistic formulation of the fluid dynamical equations, including the relativistic version of the Second Principle of thermodynamics.