Influence of EUP on Hawking-Page transition of BTZ black hole

In this paper, we investigate the influence of the extended uncertainty principle (EUP) on the Hawking-Page (HP) of the famous BTZ black hole. For the non-rotating BTZ black hole, the HP transition emerges because of the EUP effect, while there is no HP transition for this static BTZ black hole in Einstein gravity. The EUP parameter α decreases the HP transition temperature. Especially, this HP transition is abnormal, as it involves a phase transition from a high-temperature thermal vacuum state to a low-temperature AdS black hole state, in contrast to the standard HP transition (where the low-temperature vacuum and high-temperature black-hole phases are more stable). For the rotating BTZ black hole, there is always a standard HP transition which is the same as in the case in Einstein gravity. We find that the EUP parameter α reduces the black hole radius at the HP transition point while increasing the HP transition temperature, opposite to its effect on the non-rotating case. The notable quantum corrections to the HP transition of BTZ black holes may bring some clues about the understanding of the quantum properties of gravity.