Pseudo-Schwarzschild description of transonic spherical accretion onto compact objects

Abstract

A number of \modied Newtonian potentials of various forms are available in the literature which accu- rately approximate some general relativistic eects important for studying accretion discs around a Schwarzschild black hole. Such potentials may be called \pseudo-Schwarzschild potentials because they nicely mimic the space- time around a non-rotating/slowly rotating compact object. In this paper, we examine the validity of the appli- cation of some of these potentials to study the spherically symmetric, transonic, hydrodynamic accretion onto a Schwarzschild black hole. By comparing the values of various dynamical and thermodynamic accretion parameters obtained for flows using these potentials with full general relativistic calculations, we have shown that though the potentials discussed in this paper were originally proposed to mimic the relativistic eects manifested in disc accretion, it is quite reasonable to use most of the potentials in studying various dynamical as well as thermody- namic quantities for spherical accretion to compromise between the ease of handling of a Newtonian description of gravity and the realistic situations described by complicated general relativistic calculations. Also we have shown that depending on the chosen regions of parameter space spanned by specic energyE and adiabatic index of the flow, one potential may have more importance than another and we could identify which potential is the best approximation for full general relativistic flow in Scwarzschild space-time for particular values ofE and .