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Quantum Fields in Curved Space N. D. Birrell, P. C. W. Davies
Publisher: Cambridge University Press

A new improved criterion for the validity of First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Then, there is the problem of quantization. Since the gravitational field is determined by the curvature of spacetime, that would mean on small scales, space would not be continuous and smooth, but rather would be violently curved and fluctuating up and down. Usually the semiclassical expansion is formulated using the background field method of quantum field theory (QFT) in Lagrangian framework [3–6]. Quantum field theory in curved spacetime predicts that event horizons emit radiation like a black body with a finite temperature. Its also in the lecture series he gave, “Quantum FIeld Theory in Curved Spacetime and Black Hole Thermodyanmics”. But if you want to know things like the rate of radiation and the Temperature spectrum of what comes out, you need to do quantum field theory (QFT) in curved spacetime. Strings in curved background is a well-studied problem [1, 2]. Nameless says: November 21, 2012 at 4:48 pm. I can't do the math, but I suspect that gravity waves from distant events are unlikely to penetrate spacetime that is locally curved by strong gravitational fields. The noise kernel is the vacuum expectation value of the (operator-valued) stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. Taking this into effect, then, requires, at the very least, a massive rewriting of quantum mechanics, as it could no longer treat space and time as fixed parameters.