Quantum field theory in curved spacetime

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Quantum field theory in curved spacetimes is an extension of standard quantum field theory to curved spacetimes. A general prediction of this theory is that particles can be created in strong gravitational fields.

Thanks to the equivalence principle the quantization procedure closely resembles that of Minkowski spacetime once the proper formalism is chosen; however, interesting new phenomena occur. In general, on curved spacetimes quantum fields lose their interpretation as particles. Only in certain situations, such as in asymptotically flat spacetimes, can the notion of particle be recovered. Even then, the particle interpretation depends on the observer (ie, different observers may measure different numbers of particles on a given spacetime). The prediction that gravitational fields can create particles is partly due to this ambiguity.

Probably the most striking application of the theory of quantum fields in curved spacetime is Hawking's prediction that black holes radiate with a thermal spectrum. A related prediction is the Unruh effect: accelerated observers in the vacuum measure a thermal bath of particles.

This formalism is also used to predict the primordial density perturbation spectrum arising from cosmic inflation. Since this spectrum is measured by a variety of cosmological measurements -- such as the CMB -- if inflation is correct this particular prediction of the theory has already been verified.

The theory of quantum field theory in curved spacetime can be considered as a first approximation of the inaccessible theory of quantum gravity. A second step towards that theory would be semiclassical gravity, which would include the influence of particles created by a strong gravitational field on the spacetime (which is still considered classical).

[edit] Suggested reading

• R.M. Wald. Quantum field theory in curved space-time and black hole thermodynamics. Chicago U. (1995).
• S.A. Fulling. Aspects of quantum field theory in curved space-time. CUP (1989).
• N.D. Birrell & P.C.W. Davies. Quantum fields in curved space. CUP (1982).