Black hole echos reflect the phase transition and fluctuations in Hawking radiation

Black holes are thermal objects. They can form thermodynamic phases and exhibit phase transitions. Furthermore, black holes can also radiate, termed as Hawking radiation. However, the signatures of these behaviors are challenging to observe. In this work,we consider Hawking radiation in black hole phase transitions. We uncovered that an echo can emerge from the correlations between individual single event and joint two events. This provides possible signature of black hole phase transition and fluctuations in Hawking radiation.