Entropy for quantum fields in curved space time

Autor(en)

Heide Narnhofer

Abstrakt

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 spacetime and its extension to the Kruskal spacetime. The quantum field on the Schwarzschild spacetime has infinite entropy, even if we regularize over the horizon. Nevertheless, for domains in the Schwarzschild spacetime, 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 infinity.

Organisation(en)

Mathematische Physik

Journal

Classical and Quantum Gravity

Band

28

Anzahl der Seiten

12

ISSN

0264-9381

DOI

https://doi.org/10.1088/0264-9381/28/14/145016

Publikationsdatum

2011

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/4ded78e2-5fb5-40d7-a9ef-1ba2d2d5c66f