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Michel accretion of a polytropic fluid with adiabatic index gamma > 5/3: Global flows versus homoclinic orbits

We analyze the properties of a polytropic fluid which is radially accreted into a Schwarzschild black hole. The case where the adiabatic index gamma lies in the range 1 < gamma <= 5/3 has been treated in previous work. In this article we analyze the complementary range 5/3 < gamma <= 2. To this purpose, the problem is cast into an appropriate Hamiltonian dynamical system whose phase flow is analyzed. While for 1 < gamma <= 5/3 the solutions are always characterized by the presence of a unique critical saddle point, we show that when 5/3 < gamma <= 2, an additional critical point might appear which is a center point. For the parametrization used in this paper we prove that whenever this additional critical point appears, there is a homoclinic orbit.