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The minus sign in the first law of de Sitter horizons

Published version
Peer-reviewed

Repository DOI


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Authors

Banihashemi, Batoul  ORCID logo  https://orcid.org/0000-0002-2867-9209
Jacobson, Ted 
Svesko, Andrew 

Abstract

jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pDue to a well-known, but curious, minus sign in the Gibbons-Hawking first law for the static patch of de Sitter space, the entropy of the cosmological horizon is jats:italicreduced</jats:italic> by the addition of Killing energy. This minus sign raises the puzzling question how the thermodynamics of the static patch should be understood. We argue the confusion arises because of a mistaken interpretation of the matter Killing energy as the total internal energy, and resolve the puzzle by introducing a system boundary at which a proper thermodynamic ensemble can be specified. When this boundary shrinks to zero size the total internal energy of the ensemble (the Brown-York energy) vanishes, as does its variation. Part of this vanishing variation is thermalized, captured by the horizon entropy variation, and part is the matter contribution, which may or may not be thermalized. If the matter is in global equilibrium at the de Sitter temperature, the first law becomes the statement that the generalized entropy is stationary.</jats:p>

Description

Keywords

4902 Mathematical Physics, 49 Mathematical Sciences, 51 Physical Sciences

Journal Title

Journal of High Energy Physics

Conference Name

Journal ISSN

1126-6708
1029-8479

Volume Title

Publisher

Springer Science and Business Media LLC