Influence of matter geometry on shocked flows-I: Accretion in the   Schwarzschild metric
  This work presents a comprehensive and extensive study to illustrate how the geometrical configurations of low angular momentum axially symmetric general relativistic matter flow in Schwarzschild metric may influence the formation of energy preserving shocks for adiabatic/polytropic accretion as well as of temperature preserving dissipative shocks for for the isothermal accretion onto non-rotating astrophysical black holes. The dynamical and thermodynamic states of post shock polytropic and isothermal flow have been studied extensively for three possible matter geometries, and it has been thoroughly discussed about how such states depend on the flow structure, even when the self gravity and the back reaction on the metric are not taken into account. Main purpose of this paper is thus to mathematically demonstrate that for non-self gravitating accretion, various matter geometry, in addition to the corresponding space-time geometry, controls the shock induced phenomena as observed within the black hole accretion discs. This work is expected to reveal how the shock generated phenomena (emergence of the outflows/flare or the behaviour of QPO of the associated light curves) observed at the close proximity of the horizon depends on the physical environment of the source harbouring a supermassive black hole. 
Pratik Tarafdar and Tapas Kumar Das
gr-qc