For even convex polynomially bounded dispersion relations, an effective horizon controls the outgoing modes so that Bogoliubov coefficients agree with the tunneling result and the emission spectrum deviates from exact thermality in a controlled way.
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Hawking radiation with dispersion: reconciling the Bogoliubov and tunneling approaches
For even convex polynomially bounded dispersion relations, an effective horizon controls the outgoing modes so that Bogoliubov coefficients agree with the tunneling result and the emission spectrum deviates from exact thermality in a controlled way.