One of the new methods that can be used to study the thermodynamics, critical points of a
system based on a topological approach is the study of topological charges using Duan's ϕ-
mapping method. In this article, we will attempt to use this method to study three different
black holes, each with different coefficients in their metric function, in order to determine the
class of critical points, these black holes have in terms of phase transition. Through this
analysis, we found that the Euler–Heisenberg black hole has two different topological …