Notes on peculiarities of quantum fields in space–times with horizons

Abstract

We consider a massive scalar field theory on static four-dimensional space-times with horizons. We study the near horizon behaviour of the quantum expectation values of the stress--energy tensor operator for the thermal states with arbitrary temperatures. It turns out that the dependence of the expectation values on the temperature and tensor structure of the stress--energy tensor are different from the usual ones in the Minkowski space-time. Moreover, for non--canonical temperatures these expectation values are divergent on the horizons. We also show that the Wightman functions have additional infrared peculiarities near the horizons.

Is the Euclidean path integral always equal to the thermal partition function?

“…In space-times with Killing horizons, one can also consider a thermal gas with the planckian density matrix with an arbitrary temperature, different from the canonical one. But if the temperature is different from the canonical one, then correlation functions do not posses Hadamard properties on Killing horizons and the back-reaction on the background geometry is strong (see, for example: [37][38][39][40][41][42][43][44][45]). Furthermore, the thermalization process in curved space-times, in general, is far from being well understood [46].…”

The propagator matrix reloaded

“…Once more this is a very physical quantity to calculate as it is often the object of interest in, e.g. cosmological applications [29][30][31][32][33][34][35][36][37][38][39][40][41][42].…”

“…In this case, the main phenomenology is that of secular growth, that is, loop corrections which grow linearly in time, seemlingly ruining perturbation theory at late times. These kinds of issues are well known in the finite temperature literature [9-12, 18, 21-28] and in the case of de Sitter spacetime [29][30][31][32][33][34][35][36][37][38][39][40][41][42]. There have been some calculations performed in black hole and Rindler scenarios [26,[42][43][44][45][46][47] but the status is less clear in these cases.…”

“…These kinds of issues are well known in the finite temperature literature [9-12, 18, 21-28] and in the case of de Sitter spacetime [29][30][31][32][33][34][35][36][37][38][39][40][41][42]. There have been some calculations performed in black hole and Rindler scenarios [26,[42][43][44][45][46][47] but the status is less clear in these cases. In order to handle these divergences one needs to construct a modified effective field theory which can take into account the open system character of theories at finite temperature and in the presence of event horizons [29,30,33,34,[37][38][39][40].…”

Quantization of spinor field in the Schwarzschild spacetime and spin sums for solutions of the Dirac equation

“…It should be noted that there are already papers (see, for example, recent papers [11][12][13]), in which the quantum scalar field is considered only outside the event horizon of the Schwarzschild black hole. Nevertheless, despite the fact that, in some rigorous methods for constructing quantum theory in the gravitational field of a black hole, it is not necessary to take into account the internal regions of black and white holes, the question remains whether it is possible to construct a consistent quantum field theory in the Schwarzschild spacetime only above the horizon.…”