Abstract
In this paper we study the gravitational effects induced by the quantum fluctuations of the energy–momentum tensor of scalar fields. Our treatment is based on the two-point correlation function of this operator. In a large N limit, this treatment constitutes the next contribution after the semiclassical treatment. The specific example we study are the gravitational interactions between outgoing configurations giving rise to Hawking radiation and in-falling configurations. Even when the latter are in vacuum state, the interactions grow boundlessly upon approaching the horizon. Their main effect is to wash out the trans-Planckian correlations which existed in a given background geometry. When evaluated in the lowest order, these interactions express themselves in terms of a stochastic ensemble of metric fluctuations. The propagation of Hawking radiation in this ensemble resembles that of sound propagation in a random medium. The analogies with acoustic black holes are manifest even though certain features differ.
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Parentani, R. Toward a Collective Treatment of Quantum Gravitational Interactions. International Journal of Theoretical Physics 40, 2201–2216 (2001). https://doi.org/10.1023/A:1012982103523
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DOI: https://doi.org/10.1023/A:1012982103523