Constraints via the Event Horizon Telescope for Black Hole Solutions with Dark Matter under the Generalized Uncertainty Principle Minimal Length Scale Effect

Abstract

Four spherically symmetric but non-asymptotically flat black hole solutions surrounded with spherical dark matter distribution perceived under the minimal length scale effect is derived via the generalized uncertainty principle. Here, the effect of this quantum correction, described by the parameter gamma, is considered on a toy model galaxy with dark matter and the three well-known dark matter distributions: the cold dark matter, scalar field dark matter, and the universal rotation curve. The aim is to find constraints to gamma by applying these solutions to the known supermassive black holes: Sagittarius A (Sgr. A*) and Messier 87* (M87*), in conjunction with the available Event Horizon telescope. The effect of gamma is then examined on the event horizon, photonsphere, and shadow radii, where unique deviations from the Schwarzschild case are observed. As for the shadow radii, bounds are obtained for the values of gamma on each black hole solution at 3 sigma confidence level. The results revealed that under minimal length scale effect, black holes can give positive (larger shadow) and negative values (smaller shadow) of gamma, which are supported indirectly by laboratory experiments and astrophysical or cosmological observations, respectively. This paper explores the impact of the generalized uncertainty principle on black hole solutions with spherical dark matter distributions. It examines the parameter gamma and its influence on supermassive black holes like Sgr. A* and M87*, utilizing data from the Event Horizon telescope. The study reveals unique deviations in event horizon and shadow radii, providing bounds on gamma at the 3 sigma confidence level. These findings have implications for laboratory experiments and astrophysical observations, reshaping the understanding of black holes.image