A Fluid-Membrane Description of the BTZ Black Hole

Abstract: The 2+1 dimensional Banados-Teitelboim-Zanelli (BTZ) black hole has proved to be a remarkably efficient tool to test ideas about quantum aspects of gravity and holography. Here, we provide a classical fluid-membrane description of this geometry, both in static and rotating versions, that defines a dynamical viscous Newtonian fluid with non-trivial transport coefficients, mimicking the black hole. The membrane paradigm for black holes in four or more dimensions usually yields fluids with a negative bulk viscosity, which is a problem because it yields decreasing total entropy in thermal processes according to Stokes' hypothesis. However, the (rotating) BTZ black hole has a zero bulk viscosity and is amenable to a physically viable fluid membrane description at thermal equilibrium.