几何流和宇宙学孤子解的Constantin Carathéodory公理化方法和Grigory Perelman热力学
Constantin Carathéodory axiomatic approach and Grigory Perelman thermodynamics for geometric flows and cosmological solitonic solutions
摘要：
我们详细阐述了相对论几何流的统计热力学模型，作为G. Perelman和R. Hamilton理论以C.热力学的Carathéodory公理化方法与Pfweian微分方程。发展了非完整标架变形方法AFDM，用于构造相对论几何流和广义相对论中一般的非对角和局部各向异性宇宙学孤子解。我们的结论是，这样的解决方案不能描述的霍金-贝肯斯坦热力学的超曲面，全息，（反）德西特和类似的配置。的几何热力学值的定义和计算非完整的里奇流，（修改）爱因斯坦方程，和新的类的局部各向异性的宇宙学解编码孤子的层次。
英文摘要：
We elaborate on statistical thermodynamics models of relativistic geometric flows as generalisations of G. Perelman and R. Hamilton theory centred around C. Carathéodory axiomatic approach to thermodynamics with Pfaffian differential equations. The anholonomic frame deformation method, AFDM, for constructing generic off--diagonal and locally anisotropic cosmological solitonic solutions in the theory of relativistic geometric flows and general relativity is developed. We conclude that such solutions can not be described in terms of the Hawking--Bekenstein thermodynamics for hypersurface, holographic, (anti) de Sitter and similar configurations. The geometric thermodynamic values are defined and computed for nonholonomic Ricci flows, (modified) Einstein equations, and new classes of locally anisotropic cosmological solutions encoding solitonic hierarchies.
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