Photon region and shadow of a rotating 5D black string

TL;DR

This paper investigates the shadow of a rotating 5D black string in General Relativity, analyzing photon motion along the extra dimension and using EHT observations to constrain the size of the extra dimension.

Contribution

It introduces a novel analysis of photon regions and shadows in 5D black strings considering extra-dimensional photon momentum, and constrains the extra dimension size using EHT data.

Findings

Photon region and shadow are enlarged by extra-dimensional photon momentum.

EHT observations exclude infinite-length black strings, favoring compact extra dimensions.

The extra dimension length is constrained to approximately 2-2.6 mm.

Abstract

To explore the possible clues for the extra dimension from the Event Horizon Telescope (EHT) observations, we study the shadow of the rotating 5D black string in General Relativity (GR). Instead of investigating the shadow in the effective 4D theory, we concern the motion of photons along the extra dimension $z$ with a conserved momentum $P_z$, which appears as an effective mass in the geodesic equations of photons. The existence of $P_z$ enlarges the photon regions and the shadow of the rotating 5D black string while it has slight impact on the distortion. The EHT observations of M87* and SgrA* can rule out the black string model with an infinite length along the extra dimension, and support the hypothesis that the extra dimension is compact to avoid the Gregory-Laflamme (GL) instability, where the length of the black string/the compact extra dimension can be constrained as $2.03125~\rm{mm} \lesssim \ell \lesssim 2.6~\rm{mm}$ and $2.28070~\rm{mm} \lesssim \ell \lesssim 2.6~\rm{mm}$ respectively.