The Black Hole Idealization Paradox

Stephen Hawking's derivation of Hawking radiation relied on one particular spacetime model, that of a star collapsing into a black hole which then remains in existence forever. He then argued that Hawking radiation implies this model should be thrown away in favour of a different model, that of an evaporating black hole. This aspect of Hawking's argument is an example of an idealization that is pervasive in the literature on black hole thermodynamics, but which has not yet been widely discussed by philosophers. The aim of this paper is to clarify the nature of Hawking's idealization, and to show a sense in which it leads to a paradox. After identifying this idealization paradox in classic derivations of Hawking radiation, I go on to show how various research programmes in black hole thermodynamics can be viewed as possible resolutions to the paradox. I give an initial analysis of the prospects for success of these various resolutions, and show how they shed light on both the philosophical foundations of both Hawking radiation on the nature of idealizations in physics.