Pseudo-Schwarzschild description of transonic spherical accretion onto compact objects

A number of "modified" Newtonian potentials of various forms are available in the literature which accurately approximate some general relativistic ef fects important for studying accretion discs around a Schwarzschild black h ole. Such potentials may be called "pseudo-Schwarzschild" potentials becaus e they nicely mimic the spacetime around a non-rotating/slowly rotating com pact object. In this paper, we examine the validity of the application of s ome of these potentials to study the spherically symmetric, transonic, hydr odynamic accretion onto a Schwarzschild black hole. By comparing the values of various dynamical and thermodynamic accretion parameters obtained for f lows using these potentials with full general relativistic calculations, we have shown that though the potentials discussed in this paper were origina lly proposed to mimic the relativistic effects manifested in disc accretion , it is quite reasonable to use most of the potentials in studying various dynamical as well as thermodynamic quantities for spherical accretion to co mpromise 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 p arameter space spanned by specific energy E and adiabatic index gamma of th e ow, one potential may have more importance than another and we could iden tify which potential is the best approximation for full general relativisti c ow in Scwarzschild space-time for particular values of E and gamma.