In the region where the gravitational field is strong, we have examined the influence of different gravities on the accretion disk formed due to spherical accretion. To achieve this, we obtain numerical solutions of the GRH equations, utilizing Schwarzschild, Kerr, Einstein–Gauss–Bonnet, and Hartle–Thorne spacetime metrics. We investigate the impact of the rotation parameter of a black hole ([Formula: see text]), the EGB coupling constant ([Formula: see text]), and the quadrupole moment of the rotating black hole (q) on the accretion disk formed in a strong field. The formation of the disk for the slowly and rapidly rotating black hole models is separately examined, and comparisons are made. Our numerical simulations reveal that, under the specific conditions, the solution derived from Hartle–Thorne gravity converges toward solutions obtained from Kerr and other gravitational models. In the context of the slowly rotating black hole with [Formula: see text], we observe a favorable agreement between the Hartle–Thorne result and the Kerr result within the range of [Formula: see text]. Conversely, in the scenario of the rapidly rotating black hole, a more pronounced alignment with the value of [Formula: see text] is evident within the range of [Formula: see text]. Nevertheless, for [Formula: see text], it becomes apparent that the Hartle–Thorne solution diverges from solutions provided by all gravitational models. Our motivation here is to utilize the Hartle–Thorne spacetime metric for the first time in the numerical solutions of the GRH equations for the black holes, compare the results with those obtained using other gravities, and identify under which conditions the Hartle–Thorne solution is compatible with known black hole spacetime metric solutions. This may allow us to provide an alternative perspective in explaining observed X-ray data.
