TY - JOUR

T1 - The Penrose inequality and the fluid/gravity correspondence

AU - Oz, Yaron

AU - Rabinovich, Michael

PY - 2011

Y1 - 2011

N2 - Motivated by the fluid/gravity correspondence, we consider the Penrose inequality in the framework of fluid dynamics. In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by some Cauchy data, it suggests a creation of a naked singularity, thus providing means to consider the cosmic censorship hypothesis. The analogous inequality in the context of fluid dynamics can provide a valuable tool in the study of finite-time blowups in hydrodynamics. We derive the inequality for relativistic and nonrelativistic fluid flows in general dimension. We show that the inequality is always satisfied at the ideal fluid order. At the leading viscous order, the inequality may be violated by relativistic fluid flows, while it is always satisfied by nonrelativistic incompressible flows. The inequality may be violated at the next to leading viscous order by both relativistic and nonrelativistic flows.

AB - Motivated by the fluid/gravity correspondence, we consider the Penrose inequality in the framework of fluid dynamics. In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background. If the inequality is violated by some Cauchy data, it suggests a creation of a naked singularity, thus providing means to consider the cosmic censorship hypothesis. The analogous inequality in the context of fluid dynamics can provide a valuable tool in the study of finite-time blowups in hydrodynamics. We derive the inequality for relativistic and nonrelativistic fluid flows in general dimension. We show that the inequality is always satisfied at the ideal fluid order. At the leading viscous order, the inequality may be violated by relativistic fluid flows, while it is always satisfied by nonrelativistic incompressible flows. The inequality may be violated at the next to leading viscous order by both relativistic and nonrelativistic flows.

KW - Gauge-gravity correspondence

KW - Holography and quark-gluon plasmas

UR - http://www.scopus.com/inward/record.url?scp=80053123720&partnerID=8YFLogxK

U2 - 10.1007/JHEP02(2011)070

DO - 10.1007/JHEP02(2011)070

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AN - SCOPUS:80053123720

SN - 1126-6708

VL - 2011

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 2

M1 - 70

ER -