A Thermality & Nonthermality of Radiation in Curved Spacetimes

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The discussion focuses on the thermal and non-thermal characteristics of Hawking-Unruh radiation in curved spacetimes, particularly in non-inertial frames. Some researchers categorize radiation as non-thermal or approximately thermal if it deviates from a Planckian distribution, complicating the association of a characteristic temperature. Conversely, others argue that thermality can still be present even without Planckian features, as demonstrated by the asymptotic behavior of Unruh-DeWitt detectors reaching a Gibbs thermal state. This divergence in definitions leads to confusion regarding the distinction between thermality and non-thermality in the context of acceleration and Hawking radiation. Clarifying these concepts is essential for understanding the nature of radiation in curved spacetimes.
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I have been reading some material related to the thermal and non-thermal features of Hawking-Unruh radiation. It seems some authors label any radiation that emanates within curved spacetimes (including non-inertial frames) either as non-thermal or approximately thermal if it doesn't follow a typical Planckian character, which in other words means it is hard to associate a characteristic temperature with the radiation. https://doi.org/10.1103/PhysRevD.96.025023, https://doi.org/10.1007/JHEP07(2015)009. On the other hand, some associate thermality with the radiation even if it doesn't display Planckian feautures. In one of the papers, e.g., https://arxiv.org/abs/2101.11933 , authors say the thermality is when an Unruh-DeWitt detector asymptotically reaches a Gibbs thermal state (with connections to Kubo-Martin-Schwinger condition) without having anything to do with Planckian distribution. I am totally confused how to draw the line between thermality and non-thermality of acceleration/Hawking radiation.
 
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