Relativistic Bondi-Michel accretion: global vs. homoclinic solutions

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Written by Patryk Mach

A spherically symmetric accretion model introduced by Bondi in 1952 belongs to classical textbook models of theoretical astrophysics. Its general relativistic version is due to Michel, who considered spherically symmetric, purely radial, stationary flow of perfect fluid in the Schwarzschild spacetime. Solutions of the Bondi-Michel flow are usually parametrized by fixing asymptotic values of the density and the speed of sound at infinity; they extend smoothly from infinity up to the horizon of the black hole (and below). In contrast to that, local solutions, that cannot be extended to infinity, were recently discovered in the cosmological context. They correspond to homoclinic orbits on phase diagrams of the radial velocity vs. radius (say). More surprisingly, they also appear in the standard Bondi-Michel model for polytropic fluids with polytropic exponents larger than 5/3. In this talk I will discuss recent results on the existence of those local, homoclinic solutions.