具有非线性扩散的等离子体球和黑洞的简化
Simplifying plasma balls and black holes with nonlinear diffusion
摘要：
在作者的硕士论文中，我们研究了从全息规范理论的随机玩具模型中出现的引力物理的某些方面。我们首先回顾场论热力学，黑洞热力学和如何AdS / CFT对应提供了两者之间的联系。然后，我们研究了一个非线性演化方程的能量密度，这是去年从一个随机行走的状态密度。当一个维度是非紧致的，各种场论会产生与黑洞对偶的长寿等离子体球。这是由于与Hagedorn态密度相关的捕获现象。数值和数学结果的帮助下，我们表明，当两个或两个以上的维度是非紧的问题。我们的模型的一个自然的扩展涉及到一个系统的能量和动量的偏微分方程。我们的第二个模型被证明有一些理想的，但也有一些不希望的属性，如潜在的分歧与流体力学。
英文摘要：
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.
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