# Local Thermal Equilibrium and KMS states in Curved Spacetime

Christoph Solveen
November 02, 2012
On the example of a free massless and conformally coupled scalar field, it is argued that in quantum field theory in curved spacetimes with time-like Killing field, the corresponding KMS states (generalized Gibbs ensembles) at parameter $\beta>0$ need not possess a definite temperature in the sense of the zeroth law. In fact, these states, although passive in the sense of the second law, are not always in local thermal equilibrium (LTE). A criterion characterizing LTE states with sharp local temperature is discussed. Moreover, a proposal is made for fixing the renormalization freedom of composite fields which serve as "thermal observables" and a new definition of the thermal energy of LTE states is introduced. Based on these results a general relation between the local temperature and the parameter \beta is established for KMS states in (Anti) de Sitter spacetime.
open access link Class. Quantum Grav. 29 (2012) 245015
@article{Solveen:2012ai, author = "Solveen, Christoph", title = "{Local Thermal Equilibrium and KMS states in Curved Spacetime}", journal = "Class. Quant. Grav.", volume = "29", year = "2012", pages = "245015", doi = "10.1088/0264-9381/29/24/245015", eprint = "1211.0431", archivePrefix = "arXiv", primaryClass = "gr-qc", SLACcitation = "%%CITATION = ARXIV:1211.0431;%%" }

Keywords:
local thermal equilibrium, QFT on curved spacetimes