Analysis of regular black hole with multi-polytropic equation of state under various backgrounds Farzan Mushtaq, Xia Tiecheng, Allah Ditta and Badr S. Alkahtani Eur. Phys. J. Plus, 140 5 (2025) 440 Published online: 24 May 2025 DOI: 10.1140/epjp/s13360-025-06349-2