# Gubser-Mitra conjecture The Gubser-Mitra conjecture states that a black brane with a noncompact translational symmetry is classically stable if, and only if, it is locally thermodynamically stable. ## Thermodynamic stability > The definition of local thermodynamic stability adopted by GM was the one used in [[Gubser1998]], namely that the Hessian of the entropy with respect to the other extensive thermodynamic variables (i.e. mass and charges) should be negative definite. This is the mathematical statement of the condition that it shouldn’t be possible for the system to gain entropy by splitting into several parts whilst conserving energy and charge, i.e., it is a statement about the microcanonical ensemble. -- [[2001#Reall]] ## Refs - OG [[GubserMitra200009]] & [[GubserMitra200011]] - proof - [[2001#Reall]] - important - [[GubserOzakin2003]] - relation to sound speed - [[Buchel2005]] - review - [[HarmarkNiarchosObers2007Review]][](https://arxiv.org/abs/hep-th/0701022) ## Relation to [[0325 Quasi-normal modes|QNM]] - [701-706] of [[2009#Berti, Cardoso, Starinets (Review)]]