https://doi.org/10.1140/epjp/s13360-025-06349-2
Regular Article
Analysis of regular black hole with multi-polytropic equation of state under various backgrounds
1
Department of Mathematics, Shanghai University, Shanghai, People’s Republic of China
2
Newtouch Center for Mathematics of Shanghai University, 200444, Shanghai, People’s Republic of China
3
Department of Mathematics, School of Science, University of Management and Technology, 54000, Lahore, Pakistan
4
Research Center of Astrophysics and Cosmology, Khazar University, 41 Mehseti Street, 1096, Baku, Azerbaijan
5
Department of Mathematics, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia
a
xiatc@shu.edu.cn
b
mradshahid01@gmail.com
Received:
13
March
2025
Accepted:
18
April
2025
Published online:
24
May
2025
The purpose of this work is to examine the weak deflection angle, shadow, Regge–Wheeler potential, and greybody factor of a black hole with a multi-polytropic equation of state. In the weak field limit, we use the Gauss–Bonnet theorem along with the Gibbons and Werner method to find the photon’s ray’s deflection angle. Furthermore, we demonstrate how plasma and non-plasma mediums behave with respect to the deflection of photons. Similarly, we examine the graphical effects of the deflection angle on a black hole with a multi-polytropic equation of state, by considering both plasma and non-plasma medium. We also investigate the shadow of a black hole using a multi-polytropic equation of state. Furthermore, we improve our interest by including the spin-dependent Regge–Wheeler potential, which determines the dynamics of perturbations in the presence of the polytropic equation of state black hole. Our analysis of the Regge–Wheeler potential for different spin fields reveals the impact of parameters on its form when monopoles are present. Our study also focused on the rigorous bounds of the black hole with respect to the greybody factor, as well as its graphical behaviour.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
