Employing shadow radius to constrain extra dimensions in black string space-time with dark matter halo

TL;DR

This paper investigates how the shadow of five-dimensional black strings in dark matter environments can be used to constrain properties of extra dimensions, providing specific bounds on parameters like the shadow radius, extra length, and compactness.

Contribution

It introduces a method to constrain extra-dimensional parameters using black string shadow observations, considering dark matter effects and the momentum characteristic of the extra dimension.

Findings

Constraint range for momentum parameter: 0 to ~0.171215

Effective extra length range: 2.16138 mm to 2.6 mm

Impact of extra dimension momentum on dark matter parameter constraints

Abstract

We study the shadow of five-dimensional black strings immersed in dark matter environment. We show the influence of the momentum characteristic parameter $\widetilde{P_{y}}$ of the extra compact dimension on the shadow radius, and we provide the constraint range $0~\leq~\widetilde{P_{y}}~\lesssim~0.171215$ in the static Schwarzschild black string solution based on the observed data. Furthermore, we give the effective range $2.16138~\text{mm}~\lesssim~\ell~<~2.6~\text{mm}$ for the extra length $\ell$ and $\mathrm{k}~\lesssim~0.07398$ for the compactness parameter $\mathrm{k}$ in the environment near a black hole. We also find that the momentum characteristic parameter $\widetilde{P_{y}}$ of extra dimension will affect the effective range of dark matter related parameters when using shadow radius as a constraint tool.