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

TL;DR

This paper derives black hole solutions influenced by dark matter and quantum effects under the generalized uncertainty principle, using observational data from the Event Horizon Telescope to constrain the quantum correction parameter.

Contribution

It introduces new black hole solutions incorporating dark matter and minimal length scale effects, and constrains the quantum parameter using real astronomical observations.

Findings

Bounds on the quantum correction parameter $b$ at 3$c$ confidence level.

Deviations in black hole shadow sizes due to quantum effects.

Support for positive and negative $b$ values from astrophysical data.

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.