I have heard a lot of times (see e.g. papers like [1, 2]) that GR is not renormalizable and breaks down at energies at the scale of the Planck Mass $M_{\text{Planck}}\sim 10^{19}$ GeV. What is the (simple) explanation for these two statements?
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1Does this answer your question? Why doesn't renormalization with a Planck-scale cutoff work for quantum gravity? – John Rennie Jan 17 '23 at 11:10
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You need to rewrite GR as a perturbative QFT and explicitly show that the coupling is $1/M_P$. You can find more details in my answer here: https://physics.stackexchange.com/a/467869/133418 – Avantgarde Jan 17 '23 at 13:24