The comparison of alternative spacetimes using the spherical accretion around the black hole

TL;DR

This study compares different spacetime metrics in modeling spherical accretion disks around black holes, revealing conditions where Hartle-Thorne spacetime aligns with Kerr and other models, and exploring implications for X-ray observations.

Contribution

First numerical application of Hartle-Thorne spacetime in solving GRH equations for black hole accretion, comparing its results with established models across different rotation and quadrupole parameters.

Findings

Hartle-Thorne solutions align with Kerr for slow rotation and low quadrupole moments.

For rapid rotation and high quadrupole moments, Hartle-Thorne diverges from other models.

Results suggest conditions where Hartle-Thorne can serve as an alternative in black hole accretion modeling.

Abstract

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.