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Clarifying how mainstream derivations establish Hawking radiation in realistic evaporating spacetimes

Determine how Hawking’s (1975), Fredenhagen and Haag’s (1990), and algebraic derivations can substantiate Hawking radiation in physically realistic evaporating black hole spacetimes that lack stationarity and other global properties assumed by the original derivations.

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Background

After analyzing three mainstream derivations, the paper argues they are evaporation‑inconsistent: key assumptions (e.g., stationarity, availability of certain Killing fields, global hyperbolicity) fail in evaporating spacetimes or in the relevant globally hyperbolic subregions.

This leaves open how, if at all, these derivations can be adapted to establish Hawking radiation in realistic, evaporating settings.

References

To conclude, we have three different derivations, each of increasing mathematical rigour, and each with open questions about how they can actually claim to be establishing Hawking radiation in physically realistic models.

— The Black Hole Idealization Paradox (2404.10028 - Ryder, 15 Apr 2024) in Section 5.2, Algebraic Approaches Fail in Evaporation‑Schwarzschild (conclusion of section)