Entropy for quantum fields in curved space time

Heide Narnhofer (1)

1 Faculty of Physics [Vienna]

We discuss that entropy can be assigned to local domains for quantum fields only if we relate it to two domains nested in one another such that the entropy includes a surface effect depending on the distance of the two domains. We give upper and lower limits for the corresponding expressions, based on assumptions on the nuclearity of the quantum field and on the existence of a scaling limit. We apply these estimates to local domains in flat space and in de Sitter space. We show that in both cases the total system is in a pure state with vanishing entropy, but also, that the entropy of domains with vanishing size tends to 0. For quantum fields on a black hole we consider the Schwarzschild space time and its extension to the Kruskal space time. The quantum field on the Schwarzschild space time has infinite entropy, even if we regularize over the horizon. Nevertheless for domains in the Schwarzschild space time the entropy tends to 0, if the size tends to 0. If however we consider domains that include the total Schwarzschild domain the entropy is always ∞.

Mots clés: Physical Sciences

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Heide Narnhofer. Entropy for quantum fields in curved space time. Classical and Quantum Gravity, 2011, 28 (14), pp.145016. ⟨10.1088/0264-9381/28/14/145016⟩. ⟨hal-00719840⟩