On the late time behavior of thermal two point function in curved space-time

We investigate the late-time behavior of the thermal two-point function for a Bose gas in a curved space-time with a Killing horizon. We demonstrate that the late-time behavior undergoes a sharp transition at a critical temperature, reminiscent of a phase transition. Contrary to expectations for typical gases, the relaxation time does not vanish at high temperatures but instead saturates to a constant value that depends on the imaginary part of the lowest quasinormal modes.