Alternative derivations of Hawking radiation implicitly assume the quantum state is regular across the horizon at arbitrarily short distances.
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verdict confidence 0.75 · credence 0.78
Derivations of Hawking radiation that bypass Hawking's original mode analysis, notably the tunneling, Euclidean, and anomaly-cancellation methods, replace the explicit appeal to exponentially blueshifted frequencies with a condition on the quantum state at the horizon. That these derivations impose regularity of the state at the horizon is not seriously disputed and is stated openly in parts of the literature: the anomaly method fixes the Hawking flux precisely by demanding regularity at the horizon, the Euclidean approach selects the Hartle-Hawking state by smoothness of the Euclidean section, and tunneling calculations assume analyticity of modes across the horizon. Because these are continuum field-theory conditions, they constrain the state on all scales, which is the sense in which critics such as Jacobson and Helfer argue that the trans-Planckian input is relocated rather than removed: the assumption that unknown short-distance physics leaves the near-horizon vacuum undisturbed is built into the boundary condition instead of appearing as an explicit high-frequency mode. The credible pushback concerns the strength qualifier, not the existence of the condition. Agulló, Navarro-Salas, Olmo, and Parker have argued that, posed covariantly, the Hawking spectrum survives an invariant Planck-scale cutoff, so that regularity may be needed only down to a finite scale rather than at arbitrarily short distances; that contention drew a published Comment and remains unresolved. The related modified-dispersion results show the spectrum is robust when short-distance physics is altered, which bears on whether the assumption matters, though not on whether the standard continuum derivations make it. On balance the claim is a fair and well-attested characterization of what these derivations assume, with residual uncertainty over whether "arbitrarily short distances" can be weakened to a finite cutoff.
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