Electrically charged black holes in F ( R )-Euler-Heisenberg theory

Drawing on the concept of the non-linear dynamics of electromagnetic fields in vacuum in terms of the Euler-Heisenberg system, a static and spherically symmetric black hole solution is derived by coupling the Euler-Heisenberg term and F ( R ) gravity. In applying the curvature singularity tools, the black hole solution induces a singular behaviour at the centre r = 0 while exhibiting a regular shape at high distances. Using the heat capacity (CQ) and the Helmholtz free energy (F), we analyse the thermodynamic stability locally and globally. Furthermore, an investigation is conducted using class tools of Geometrothermodynamics (GTs) features such as Weinhold, Ruppeiner, Hendi-Panahiyan-Eslam-Momennia (HPEM), and Quevedo to identify phase transition points associated with heat capacity, including both physical boundary points (root of the heat capacity) and second critical phase transition points (divergent points of the heat capacity). We have even examined the relevant sparsity of Hawking radiation, showing how the black hole solution behaves as a black body at specific limits. Overall, this study enhances our knowledge of the mergers of a class of non-linear dynamics of electromagnetic fields in a vacuum within F ( R ) gravity by modelling black hole solutions.