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Simplifying plasma balls and black holes with nonlinear diffusion

In the Master's thesis of the author, we investigate certain aspects of gravitational physics that emerge from stochastic toy models of holographic gauge theories. We begin by reviewing field theory thermodynamics, black hole thermodynamics and how the AdS / CFT correspondence provides a link between the two. We then study a nonlinear evolution equation for the energy density that was derived last year from a random walk governed by the density of states. When one dimension is non-compact, a variety of field theories produce long lived plasma balls that are dual to black holes. This is due to a trapping phenomenon associated with the Hagedorn density of states. With the help of numerical and mathematical results, we show that problems arise when two or more dimensions are non-compact. A natural extension of our model involves a system of partial differential equations for both energy and momentum. Our second model is shown to have some desired, but also some undesired properties, such as a potential disagreement with hydrodynamics.