Photon region and shadow of a rotating 5D black string

Zi-Yu Tang; Xiao-Mei Kuang; Bin Wang; Wei-Liang Qian

doi:10.1140/epjc/s10052-023-12015-7

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 837
https://doi.org/10.1140/epjc/s10052-023-12015-7

Regular Article - Theoretical Physics

Photon region and shadow of a rotating 5D black string

Zi-Yu Tang¹^,2^,3^a, Xiao-Mei Kuang⁴, Bin Wang⁴^,5 and Wei-Liang Qian⁴^,6^,7

¹ School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, 310024, Hangzhou, China
² School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
³ Cosmology, Gravity and Astroparticle Physics Group, Center for Theoretical Physics of the Universe, Institute for Basic Science, 34126, Daejeon, Korea
⁴ Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 225009, Yangzhou, China
⁵ School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 200240, Shanghai, China
⁶ Escola de Engenharia de Lorena, Universidade de São Paulo, 12602-810, Lorena, SP, Brazil
⁷ Faculdade de Engenharia de Guaratinguetá, Universidade Estadual Paulista, 12516-410, Guaratinguetá, SP, Brazil

^a tangziyu@ucas.ac.cn, tangziyu@ibs.re.kr

Received: 12 December 2022
Accepted: 6 September 2023
Published online: 21 September 2023

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 $P_{z}$ $$P_z$$ , which appears as an effective mass in the geodesic equations of photons. The existence of $P_{z}$ $$P_z$$ 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 $2.03125 mm ≲ ℓ ≲ 2.6 mm$ $2.03125~\textrm{mm} \lesssim \ell \lesssim 2.6~\textrm{mm}$ and $2.28070 mm ≲ ℓ ≲ 2.6 mm$ $2.28070~\textrm{mm} \lesssim \ell \lesssim 2.6~\textrm{mm}$ respectively.

© The Author(s) 2023

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