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

Strings in curved background is a well-studied problem [1, 2]. Since there is no complete quantum theory of gravity, they used an established approach called quantum field theory in curved spacetime (QFTCS). The Field Equations control the curvature of space-time and represent our theory of gravity, while the Yang-Mills and Dirac equations represent the theory of particle interactions on a quantum level. The second input is to take some spacetime manifold (like flat Minkowski space or something more curved) and attach a C*-algebra to each open subset in a compatible way. There is an entire field of study dedicated to the development of quantum field theories in general relativistic -- including time dependent -- backgrounds, called Quantum Field Theory in Curved Spacetime. And have studied quantum information transmission in the presence of a black hole. Semiclassical gravity, is the same name used for "quantum field theory in curved-spacetime" ??? 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. Even a “perfect” vacuum would still hold vacuum energy, the Higgs field, and spacetime curvature. That was based on semiclassical gravity approach??? Outer space is teaming with fields and particles. And what about the Unruh effect ???