Universal relations with the non-extensive entropy perspective

Recent advancements in black hole thermodynamics have introduced corrections to elucidate the relationship between entropy and extremality bound of black holes. Traditionally, this relationship has been studied in the context of black holes characterized by Bekenstein–Hawking entropy. However, this study extends the investigation to encompass non-extensive generalizations of entropy. We introduce a minor constant correction, denoted as $\left(\varepsilon \right)$, and examine the universal relations for a charged Anti-de Sitter (AdS) black hole. Our findings indicate that these universal relations do not hold for the charged AdS black hole when described by the non-extensive generalizations of entropy. Of course, with some adjustments, the universality relations are met. In contrast, the universal relations remain compatible when the black hole is described by Bekenstein–Hawking entropy.