Abstract This paper focuses on the Kramers escape rate, offering a dynamic approach to phase transitions in black holes. We examine the free energy landscapes under ‘dark’ and ‘stringy+dark’ influences, assessing the impact of additional parameters on escape rates and transition dynamics during first-order phase transitions from small to large black holes. We analyze the escape rate as a function of black hole radius, noting its increase from zero to a maximum point and decrease back to zero as reactive structures activate. A crucial point is where the direct process (small to large black holes) intersects with the reverse process (large to small black holes), making both equally probable. This point gains significance as the process progresses, indicating the dominance of the reverse process, which helps maintain black hole stability by preventing uncontrolled radial growth.
Afshar et al. (Wed,) studied this question.