Bumblebee AdS Black Holes in Modified Gravity (MOG)

In this study, we examine the thermodynamic properties of anti-de Sitter (AdS) black holes within the framework of Modified Gravity (MOG), a theory proposed to explain galactic dynamics without invoking dark matter. In MOG, the presence of a gravitational charge \( Q = \sqrt{\alpha G_N} M \) modifies the Newtonian constant to an effective value \( G = G_N(1 + \alpha ) \). We show that this modification leads to notable deviations from standard general relativity. Specifically, the black hole structure can feature two event horizons instead of one, and under strong MOG effects, the formation of an event horizon may be entirely suppressed, effectively eliminating the black hole. In addition, MOG can significantly modify thermodynamic functions, which in turn affect the properties of bumblebee AdS black holes; for example, MOG induces an additional phase transition. These findings highlight the significant impact of MOG on black hole thermodynamics and offer potential insights into alternative gravity scenarios.