Limitations of the pseudo-Newtonian approach in studying the accretion flow around a Kerr black hole

Abstract

We study the relativistic accretion flow in a generic stationary axisymmetric space-time and obtain an effective potential (${\mathrm{\ensuremath{\Phi}}}^{\mathrm{eff}}$) that accurately mimics the general relativistic features of Kerr black hole having spin $0\ensuremath{\le}{a}_{\mathrm{k}}<1$. Considering the accretion disc to be confined around the equatorial plane of a rotating black hole and using the relativistic equation of state, we examine the properties of the relativistic accretion flow and compare them with the same obtained form semirelativistic as well as nonrelativistic accretion flows. Towards this, we first investigate the transonic properties of the accretion flow around the rotating black hole where good agreement is observed for relativistic and semirelativistic flows. Further, we study the nonlinearities such as shock waves in accretion flow. Here also we find that the shock properties are in agreement for both relativistic and semirelativistic flows irrespective of the black hole spin (${a}_{\mathrm{k}}$), although it deviates significantly for nonrelativistic flow. In fact, when the particular shocked solutions are compared for flows with identical outer boundary conditions, the positions of shock transition in relativistic and semirelativistic flows agree well with the deviation of 6%--12% for $0\ensuremath{\le}{a}_{\mathrm{k}}\ensuremath{\le}0.99$, but vast disagreement is observed for nonrelativistic flow. In addition, we compare the parameter space [in energy ($\mathcal{E}$) and angular momentum ($\ensuremath{\lambda}$) plane] for shock to establish the fact that relativistic as well as semirelativistic accretion flow dynamics do show close agreement irrespective of ${a}_{\mathrm{k}}$ values, whereas nonrelativistic flow fails to do so. With these findings, we point out that semirelativistic flow including ${\mathrm{\ensuremath{\Phi}}}^{\mathrm{eff}}$ satisfactorily mimics the relativistic accretion flows around the Kerr black hole. Finally, we discuss the possible implications of this work in the context of dissipative advective accretion flow around Kerr black holes.