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In the last passage of 1975 paper Hawking tells that we can't use a local stress-energy tensor to tackle the backreaction of radiation since creation of particles is a non-local and global process while $T_{\mu\nu}$ is a local quantity, so we can't use it in EFE $G_{\mu\nu}=\kappa T_{\mu\nu}$ to get the dynamic nature of $g_{\mu\nu}$. Is this correct, if yes then how do we handle the backreaction problem?

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    $\begingroup$ Do you mean back-reaction rather than "backscattering"? $\endgroup$ – mmeent Oct 20 at 7:42
  • $\begingroup$ @mmeent yep! I just confused those two terms $\endgroup$ – aitfel Oct 20 at 11:00
  • $\begingroup$ Are you asking why we think black holes evaporate instead of merely radiating, and how we can estimate how long this would take? Or are you asking how we would actually implement the backreaction in a self-consistent model? Handling the backreaction in a self-consistent model requires some form of quantum gravity. More generally, a model in which a quantum entity (like the quantum field in Hawking's paper) influences a classical entity (like the classical metric field) is not self-consistent. It can be useful if we avoid situations where the self-inconsistency is prominent, but that's a hack. $\endgroup$ – Chiral Anomaly Oct 20 at 23:02
  • $\begingroup$ @ChiralAnomaly I was asking about the second part (self-consistent model of evaporation). Is the answer to such a model being self-inconsistent the same as the Lubos one (Self inconsistency of semiclassical quantum gravity) which you mentioned somewhere in your previous answers? $\endgroup$ – aitfel Oct 21 at 7:27
  • $\begingroup$ I did mention a blog post by Luboš in my answer (physics.stackexchange.com/a/492039) to the question "Difference between QFT In curved spacetime, semiclassical, and quantum gravity?". Later I found another Physics SE post which explains the reason more directly, namely Luboš's answer (physics.stackexchange.com/a/6992) to the question "What are the reasons to expect that gravity should be quantized?". $\endgroup$ – Chiral Anomaly Oct 21 at 13:50

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