Title: Idealization in Hawking Radiation: A New Paradox for Semi-Classical Black Holes

Abstract: In this paper, I argue that three mainstream derivations of Hawking radiation contain an essential idealization. They are Hawking’s original derivation, Fredenhagen and Haag’s mathematically “watertight” derivation, and the algebraic derivation of the Unruh vacuum. These derivations are carried out in a spacetime which does not model black hole evaporation, whereas, given the existence of Hawking radiation, black holes are expected to evaporate. Given the assumption of non-evaporation is unphysical, one should be able to de-idealize by removing it. However, I show that assumptions essential for the derivations breakdown in evaporation spacetimes. The idealization of non-evaporation is essential for these derivations.

First, I introduce the paradox that arises for each derivation because of this essential idealization. The paradox is distinct from standard issues of idealization in physics: usually, the soundness of physical assumptions is challenged, but here the problem is an invalid argument. Second, I discuss possible resolutions to the paradox. Hawking himself recognized the troublesome idealization and proposed an approximation regime to resolve the issue. I argue that Hawking’s proposal fails and canvas alternative resolutions, favouring a resolution which relies upon weakening the premises of Hawking’s derivation. Finally, I suggest how the paradox may teach us about how global structure encodes local structure in general relativity, the nature of Hawking radiation, and how science uses models to make progress.

#BlackHoleInitiative #BHI #BHIFoundationsSeminar #hawkingradiation #blackholes