Newtonian analogue of static general relativistic spacetimes: An extension to naked singularities

Abstract

We formulate a generic Newtonian like analogous potential for static spherically symmetric general relativistic (GR) spacetime, and subsequently derived proper Newtonian like analogous potential corresponding to Janis-Newman-Winicour (JNW) and Reissner-Nordstr\"{o}m (RN) spacetimes, both exhibiting naked singularities. The derived potentials found to reproduce the entire GR features including the orbital dynamics of the test particle motion and the orbital trajectories, with precise accuracy. The nature of the particle orbital dynamics including their trajectory profiles in JNW and RN geometries show altogether different behavior with distinctive traits as compared to the nature of particle dynamics in Schwarzschild geometry. Exploiting the Newtonian like analogous potentials, we found that the radiative efficiency of a geometrically thin and optically thick Keplerian accretion disk around naked singularities corresponding to both JNW and RN geometries, in general, is always higher than that for Schwarzschild geometry. The derived potentials would thus be useful to study astrophysical processes, especially to investigate more complex accretion phenomena in AGNs or in XRBs in the presence of naked singularities and thereby exploring any noticeable differences in their observational features from those in the presence of BHs to ascertain outstanding debatable issues relating to gravity - whether the end state of gravitational collapse in our physical Universe renders black hole (BH) or naked singularity.