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Hawking radiations are predicted from semiclassical quantum field theory, and it is sometimes said that calculations break apart at mass density $M_{planck}$.

The question is, is this true only for some Hawking radiation calculations and can be overcome by calculating differently? Or is this fundamental, showing that Hawking radiation calculations cannot be properly done with semiclassical quantum field theory?

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  • $\begingroup$ Can you expand on why do you claim it is semiclassical? $\endgroup$ – ohneVal May 8 '18 at 14:30
  • $\begingroup$ I am not explicitly well-educated on all calculations for deriving Hawking temperature but I am pretty sure that all of them assume that the energy radiated via Hawking temperature can be neglected in comparison to the mass of the blackhole, or in other words, they assume a static background metric. But the Hawking formula suggests that the amount of radiated away energy can be small only when the blackhole is large, and thus, yes, all Hawking calculations are valid only when the blackholes are large. $\endgroup$ – Dvij Mankad May 8 '18 at 14:48
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Sadly it cannot be overcome in general. The Planck mass marks the scale at which our current theories make sense on their own, that meaning that the techniques used in QFT in curved space-times don't hold anymore. Specially when it has to do with gravity. Non-linear effects (self-interactions) and back-reaction become relevant, so that treating the problem as having some background plus perturbations on top, is no longer useful and to my knowledge, no one knows how to implement a proper quantization of gravity in those scenario.

It might also help to know the relation between the Planck mass $M_{Pl}$ and the gravitational constant $G$. $$M_{Pl}=\sqrt{\frac{\hslash c}{8\pi G}}$$ Since the Einstein-Hilbert action is $$ S_{EH} = \frac{M_{Pl}^2}{2}\int d^4x \sqrt{-g} R $$ and having in mind that $M_{Pl}\approx 10^{18}$ GeV/$c^2$ you will have some trouble employing perturbation theory.

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