Several rigorous results concerning QFT in the presence of a black hole have been obtained. Indeed, the viewpoint of local quantum physics is suitable to generalize the renormalization procedure to the theory of quantum fields developed on curved backgrounds. Since the end of the eighties, the local quantum field theory approach due to Rudolf Haag and Daniel Kastler has been implemented in order to include an algebraic version of quantum field theory in curved spacetime. This is why a state which looks like a vacuum to one observer cannot look like a vacuum state to another observer it could even appear as a heat bath under suitable hypotheses. Creation operators correspond to positive frequencies, while annihilation operators correspond to negative frequencies. If t′(t) is a diffeomorphism, in general, the Fourier transform of exp will contain negative frequencies even if k > 0. This is because a mode decomposition of a field into positive and negative frequency modes is not invariant under diffeomorphisms. The concept of a vacuum is not invariant under diffeomorphisms.
Even then, as in flat spacetime, the asymptotic particle interpretation depends on the observer (i.e., different observers may measure different numbers of asymptotic particles on a given spacetime).Īnother observation is that unless the background metric tensor has a global timelike Killing vector, there is no way to define a vacuum or ground state canonically.
Only in certain situations, such as in asymptotically flat spacetimes (zero cosmological curvature), can the notion of incoming and outgoing particle be recovered, thus enabling one to define an S-matrix. For non-zero cosmological constants, on curved spacetimes quantum fields lose their interpretation as asymptotic particles. Interesting new phenomena occur owing to the equivalence principle the quantization procedure locally resembles that of normal coordinates where the affine connection at the origin is set to zero and a nonzero Riemann tensor in general once the proper (covariant) formalism is chosen however, even in flat spacetime quantum field theory, the number of particles is not well-defined locally. A general prediction of this theory is that particles can be created by time-dependent gravitational fields (multigraviton pair production), or by time-independent gravitational fields that contain horizons. In particle physics, quantum field theory in curved spacetime is an extension of standard, Minkowski space quantum field theory to curved spacetime.
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