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...e quantum field theory in curved space-time. This Ansatz already led to interesting results, the most famous being the Hawking radiation of black-holes [32]. A look through the literature (see, e.g., =-=[60, 3, 25]-=-), however, shows that predominantly free field theories were treated on curved physical backgrounds. In fact, most of the papers on interacting quantum field theories on curved space-times deal with ...

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...candidate of a vacuum state or a Wigner-type particle concept. In turn, this leads to ambiguities in the concrete determination of physical quantities. This problem was observed some time ago by Wald =-=[47]-=- in his discussion of a renormalization prescription for defining the energymomentum tensor of a quantized field on a curved spacetime M with metric tensor g = gµν. For a classical massless Klein-Gord...

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...field theory on a classical background spacetime satisfying Einstein’s equations (Birrell 6 The precise nature of the geometric boundary conditions is discussed further in Sec. V.C. and Davies, 1982; =-=Wald, 1994-=-). A quantum field theory consists of one or more oscillators at every point in space. Even a single harmonic oscillator has an infinitedimensional Hilbert space. Moreover, there are infinitely many p...

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...t vanish on C; conversely, if a Killing field, ξ a , vanishes on a two-dimensional spacelike surface, C, then C will be the bifurcation surface of a bifurcate Killing horizon associated with ξ a (see =-=[15]-=- for further discussion). An important consequence of the zeroth law is that if κ = 0, then in the “maximally extended” spacetime representing a stationary black hole, the event horizon, H, comprises...

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...f of Prop. 9.3.6 of [2], but no justification for it was provided there. 4characteristic of S is non-vanishing, there exists a p ∈ S such that ˆt A (p) = 0. By the argument given on pages 119-120 of =-=[24]-=-, it follows that there exists a t0 = 0 such that ˆ φt0 is the identity map on S. Consequently, φt0 maps each null geodesic generator of N into itself. 3 Isenberg-Moncrief Spacetimes In this Section,...

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...culated using the Unruh effect in curved spacetime or finding the periodicity in the time coordinate in the Euclidean version of the black hole metric covering the outer region. (See for example Ref. =-=[49]-=-.) In the Unruh effect one considers how an observer outside the black hole 3 , following the timelike Killing flow, would experience a quantum field that is in the Hartle-Hawking vacuum state. The Ha...

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...gy and sometimes [22] even the Yang-Mills/Maxwell charge and potential, are evaluated at infinity. In part because of this ‘mismatch’, to our knowledge the ‘physical process version’ of the first law =-=[10]-=- had not previously been established for processes which change the charge of the black hole. Since all quantities in the present treatment are defined locally at the horizon, it is now straightforwar...

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... for the difficult problem of providing a physical interpretation of the theory [183, 185]. The simplest way of dealing with this problem is to identify the elements of H+ with physical state-vectors =-=[230, 110]-=- and effectively discard the rest of state-vectors as representing unphysical or ghost states. An alternative formulation of the theory that avoids the interpretational difficulties of indefinite-metr...