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The late time accelerated expansion of the Universe demands that even inlocal galactic-scales it is desirable to study astrophysical phenomena,particularly relativistic accretion related phenomena in massive galaxies or ingalaxy mergers and the dynamics of the kiloparsecs-scale structure and beyond,in the local-galaxies in Schwarzschild-de Sitter (SDS) background, rather thanin Schwarzschild or Newtonian paradigm. Owing to the complex and nonlinearcharacter of the underlying magnetohydrodynamical equations in generalrelativistic (GR) regime, it is quite useful to have an Newtonian analogouspotential containing all the important GR features that allows to treat theproblem in Newtonian framework for study of accretion and its relatedprocesses. From the principle of conserved Hamiltonian of the test particlemotion, here, a three dimensional Newtonian analogous potential has beenobtained in spherical geometry corresponding to SDS/Schwarzschild anti-deSitter (SADS) spacetime, that reproduces almost all of the GR features in itsentirety with remarkable accuracy. The derived potential contains an explicitvelocity dependent term of the test particle that renders an approximaterelativistic modification of Newtonian like potential. The complete orbitaldynamics around SDS geometry and the epicyclic frequency corresponding to SDSmetric have been extensively studied in the Newtonian framework using thederived potential. Applying the derived analogous potential it is found thatthe current accepted value of $\Lambda \sim 10^{-56} \rm cm^{-2}$ moderatelyinfluences both sonic radius as well as Bondi accretion rate, especially forspherical accretion with smaller values of adiabatic constant and temperature,which might have interesting consequences on the stability of accretion disk inAGNs/radio galaxies.

Newtonian analogue of Schwarzschild de-Sitter spacetime: Influence on the local kinematics in galaxies