  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 (a/M), the EGB coupling constant ($\alpha$), 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 towards solutions obtained from Kerr and
other gravitational models. In the context of the slowly rotating black hole
with $a/M=0.28$, we observe a favorable agreement between the Hartle-Thorne
result and the Kerr result within the range of 0 < q < 0.5. Conversely, in the
scenario of the rapidly rotating black hole, a more pronounced alignment with
the value of q=1 is evident within the range of 0.5 < q < 1. Nevertheless, for
q > 1, 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.
