We observe that the spontaneous Hawking radiation is stationary, like blackbody radiation.” Here is a link: https://www.nature.com/articles/s41567-020-01076-0
arXiv:1809.00913
We observe that the Hawking spectrum is thermal, with the temperature predicted by Hawking.
Read more:
Juan Ramón Muñoz de Nova, Katrine Golubkov, Victor I. Kolobov, and Jeff Steinhauer, Observation of thermal Hawking radiation and its temperature in an analogue black hole, Nature 569, 688 (2019).