The Penrose Inequality and the Fluid/Gravity Correspondence

Understand

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.