Impact of loop quantum gravity on gravitational lensing, thermal fluctuations, tidal force and geodesic deviation around a black hole

Abstract This study investigates the deflection of light, Einstein rings, thermal fluctuations, and tidal force and geodesic deviation in a loop quantum black hole (LQBH) resulting from gravitational collapse. Initially, we employ the Gauss–Bonnet theorem (GBT) to examine the weak deflection angle of the LQBH. For the GBT, we used the Gibbons-Werner method to obtain the Gaussian optical curvature. We also determined the deflection angle for a spherically symmetric BH in the context of the non-plasma and plasma environments under weak field constraints. Furthermore, we graphically investigate the deflection angle of light in the scenario of the impact parameter and find that the impact parameter has a direct effect on the angle. Later, we compute the Einstein rings of the LQBH and examine the graphical impact of various parameters. Moreover, we employ corrected entropy to examine the effects of thermal fluctuations for small and large BHs. For both large and small BHs, we examine the impact of the correction terms on the thermodynamic system. We also study the geodesic deviation in LQBH, with a particular emphasis on how quantum factors affect the paths of neighboring geodesics. Angular geodesics, in contrast to radial geodesics, tend to converge as one moves away from the BH, a phenomenon that reflects the complicated consequences of space-time curvature in this scenario.