Probing Kaluza–Klein black holes with massive vector fields via thermodynamics, shadows, and accretion disks
Abstract
Abstract In this paper, we investigate the thermodynamical and optical characteristics of a black hole surrounded by massive spin-1 vector fields in the framework of Kaluza–Klein gravity. Motivated by the natural emergence of massive vector fields through the dimensional reduction of higher-dimensional gravity, we explore their role in modifying the near-horizon physics and observable signatures of black holes. These vector fields, akin to dark photons, introduce Yukawa-like corrections to the gravitational potential and mimic dark matter effects without invoking exotic particles. Our thermodynamic analysis, extended via logarithmic-corrected Barrow entropy, reveals that these fields significantly alter black hole temperature, specific heat, and Gibbs free energy. Notably, phase transitions are identified and confirmed using thermodynamic geometry tools, including Quevedo and HPEM metrics, highlighting the presence of stable remnants under quantum gravity corrections. Furthermore, we examine accretion disk structures and black hole shadow images through ray-tracing techniques under both static and infalling spherical accretion models. The direct and secondary images of the disk, as well as photon ring features, exhibit distinct deformations based on $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> and $$\lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>λ</mml:mi> </mml:math> . These modifications affect observable properties such as shadow size, intensity profiles, and lensing behavior, suggesting potential avenues for empirical testing via black hole imaging. Our findings underscore the rich phenomenology induced by massive vector fields in KK gravity, providing a unified perspective on black hole thermodynamics, dynamical stability, and observational signatures.