Pseudo-Newtonian potential for accretion disks in a modified gravity spacetime around the black hole and underlying properties

Abstract

We construct a pseudo-Newtonian potential (PNP) corresponding to a rotating black hole solution in a modified gravity (MGR) framework using a metric-based prescription. The motivation is to enable realistic accretion disk studies in MGR, where full relativistic MHD simulations remain computationally prohibitive. Effective potentials and the underlying Newtonian-like forces are derived for both massive and massless particles in the equatorial plane, relevant for disk dynamics. The reliability of the PNP is tested by comparing key orbital properties -- marginally stable, marginally bound, photon orbits and energies at marginally stable orbit radii -- with exact MGR predictions. The PNP reproduces the marginally stable and photon orbits exactly, while marginally bound orbits and specific energies deviate by less than about 7-10%. The influence of the MGR parameter on particle dynamics and effective potentials is analyzed, revealing non-trivial departures from simple Newtonian intuition. The study demonstrates that the proposed PNP accurately captures essential spatial properties of MGR spacetime and provides an efficient, physically consistent tool for investigating accretion phenomena and strong-gravity astrophysics beyond general relativity.

Figures (9)

• Figure 1: The variation of $V_{eff}(=E_m^2-R)$ as a function of $r$ for $a = 0.3$, $\lambda_m = 3.75$, $E_m = 1.1$ with different $B$.
• Figure 2: The variation of $V_{eff}(=E_m^2-R)$ as a function of $r$ for $a = 0.3$, $\lambda_m = 3.4$, $E_m = 1.9$ with different $B$.
• Figure 3: The same as in Fig. \ref{['Fig1']} except for $V^0_{eff}$.
• Figure 4: The same as in Fig. \ref{['Fig2']} except for $V^0_{eff}$.
• Figure 5: The variation of $V_{eff}(=E_m^2-R)$ as a function of $r$ for $a = 0.3$, $B = 0$, $E_m = 1.1$ with different $\lambda_{m}$.