Black brane entropy and hydrodynamics

Ivan Booth, Michal Heller, Michal Spalinski

For stationary black holes it is universally known that entropy is proportional to horizon area. It is not so clear what the relationship is for dynamical black holes. In such spacetimes the event horizon is teleologically defined while the apparent horizon is non-unique. Thus even if one believes that entropy continues to be well-defined and proportional to horizon area, there are many possible areas to choose from. In this talk I will review some recent work that examines this problem in the context of dynamical black branes in AdS spacetimes. We work in the quasi-equilibrium regime where the horizons are slowly evolving on the gravity side and on the field theory side can be described by hydrodynamics. A hydrodynamic entropy current can be defined and compared with the various horizon areas. The results show good (though not perfect) agreement. We examine the uncertainties and consider the implications for each side of the correspondence.