# Hawking radiation calculation breaking apart with mass density $M_{planck}$?

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?

• Can you expand on why do you claim it is semiclassical? – ohneVal May 8 '18 at 14:30
• 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. – Dvij Mankad May 8 '18 at 14:48

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.