Abstract
Soon after the discovery by Hawking in 1974 that a black hole formed by gravitational collapse will radiate a thermal distribution of field quanta, a number of authors showed that, in particular spacetimes, when a quantum field is in a certain “natural vacuum state,” then appropriate observers “see” a thermal distribution of particles. For the ordinary vacuum state of Minkowski spacetime, Unruh (1976) obtained such a result for accelerating observers. In extended Schwarzschild spacetime, Hartle and Hawking (1976) and Israel (1976) defined a natural vacuum state (the “Hartle-Hawking vacuum”), which is a thermal state for a static observer. Similarly, for de Sitter spacetime, Gibbons and Hawking (1977) defined the “Euclidean vacuum state” and showed that it has thermal properties for any inertial (geodesic) observer.
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References
Ashtekar, A., and Magnon, A., 1975, Quantum fields in curved space-times, Proc. Roy. Soc. Lond., A346:375.
Choquet-Bruhat, Y., 1968, Hyperbolic partial differential equations on a manifold, in: “Battelle Rencontres,” C. M. DeWitt and J. A. Wheeler, eds., Benjamin, New York.
Fulling, S. A., Narcowich, F. J. and Wald, R. M., 1981, Singularity structure of the two-point function in quantum field theory in curved spacetime. II, Ann. Phys., 136:243.
Geroch, R. P., 1970, Domain of dependence, J. Math. Phys., 11:437.
Gibbons, G.W., and Hawking, S. W., 1977, Cosmological event horizons, thermodynamics and particle creation, Phys. Rev., D15:2738.
Hartle, J. B., and Hawking, S. W., 1976, Path-integral derivation of black hole radiance, Phys. Rev. D13:2188.
Hawking, S. W., and Ellis, G. F. R., 1973, “The Large Scale Structure of Spacetime,” Cambridge University Press, Cambridge.
Israel, W., 1976, Thermo-field dynamics of black holes, Phys. Lett., 57A:107.
Kay, B. S., 1978, Linear spin-zero quantum fields in external gravitational and scalar fields, Commun. Math. Phys., 62:55.
Kay, B. S., 1985, The double-wedge algebra for quantum fields on Schwarzschild and Minkowski spacetimes, Commun. Math, Phys., 100:57.
Kay, B. S., and Wald, R. M., 1989, Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasi-free states on spacetimes with a bifurcate Killing horizon, to be published.
Reed, M., and Simon, B., 1972, “Methods of Modern Mathematical Physics, Vol. I: Functional Analysis,” Academic Press, New York.
Simon, B., 1972, Topics in functional analysis, in “Mathematics of Contemporary Physics,” R. F. Streater, ed., Academic Press, New York.
Treves, F., 1975, “Basic Linear Partial Differential Equations,” Academic Press, New York.
Unruh, W. G., 1976, Notes on black hole evaporation, Phys. Rev., D14: 870.
Unruh, W. G., and Wald, R. M., 1984, What happens when an accelerating observer detects a Rindler particle, Phys. Rev., D29:1047.
Wald, R. M., 1977, The back reaction effect in particle creation in curved spacetime, Commun. Math. Phys., 54:1.
Wald, R. M., 1978, Trace anomaly of a conformally invariant quantum field in curved spacetime, Phys. Rev., D17:1477.
Wald, R. M., 1979, Existence of the S-matrix in quantum field theory in curved spacetime, Commun. Math, Phys., 70:221.
Wald, R. M., 1974, “General Relativity,” University of Chicago Press, Chicago.
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Wald, R.M. (1990). Vacuum States in Spacetimes with Killing Horizons. In: Audretsch, J., de Sabbata, V. (eds) Quantum Mechanics in Curved Space-Time. NATO ASI Series, vol 230. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3814-1_8
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DOI: https://doi.org/10.1007/978-1-4615-3814-1_8
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