Hamiltonian formulation of relativistic magnetohydrodynamic accretion on a general spherically symmetric and static black hole: quantum effects on shock states

In this paper, our aim is to extend our earlier work [Ahmed et al. in Eur. Phys. J. C 76:280, 2016], investigating an axisymmetric plasma flow with angular momentum onto a spherical black hole. To accomplish that goal, we focus on the case in which the ideal magnetohydrodynamic approximation is valid, utilizing certain conservation laws which arise from particular symmetries of the system. After formulating a Hamiltonian of the physical system, we solve the Hamilton equations and look for critical solutions of (both in and out) flows. Reflecting the difference from the Schwarzschild spacetime, the positions of sonic points (fast magnetosonic point, slow magnetosonic point, Alfvén point) are altered. We explore several kinds of flows including critical, non-critical, global, magnetically arrested and shock induced. Lastly, we analyze the shock states near a specific quantum corrected Schwarzschild black hole and determine that quantum effects do not favor shock states by pushing the shock location outward.