拉格朗日规范理论中的对称性和守恒律及其对黑洞力学和三维引力的应用
Symmetries and conservation laws in Lagrangian gauge theories with applications to the mechanics of black holes and to gravity in three dimensions
摘要：
拉格朗日规范理论中精确守恒律的处理构成了论文第一部分的主轴。形式主义是作为一个自洽的理论，但早期的作品，主要是由上同调的结果，协变相空间方法和汉密尔顿形式主义的启发。本文在一般几何条件下研究了黑洞的物理性质，特别是第一定律，并对几种黑色物体：黑洞、弦和环进行了计算。此外，还描述了一类新的三维封闭类时曲线黑洞的几何和物理性质。论文的第二部分是第一部分对渐近分析的自然推广。我们开始与协变相空间的一般建设承认渐近保守的费用。的渐近对称代数之间的保守费用的协变泊松括号的表示，然后定义，并承认一般的中心扩展。然后详细研究了三个三维时空的渐近结构，并讨论了三维空间中量子引力的结果。
英文摘要：
The treatment of exact conservation laws in Lagrangian gauge theories constitutes the main axis of the first part of the thesis. The formalism is developed as a self-consistent theory but is inspired by earlier works, mainly by cohomological results, covariant phase space methods and by the Hamiltonian formalism. The thermodynamical properties of black holes, especially the first law, are studied in a general geometrical setting and are worked out for several black objects: black holes, strings and rings. Also, the geometrical and thermodynamical properties of a new family of black holes with closed timelike curves in three dimensions are described. The second part of the thesis is the natural generalization of the first part to asymptotic analyses. We start with a general construction of covariant phase spaces admitting asymptotically conserved charges. The representation of the asymptotic symmetry algebra by a covariant Poisson bracket among the conserved charges is then defined and is shown to admit generically central extensions. The asymptotic structures of three three-dimensional spacetimes are then studied in detail and the consequences for quantum gravity in three dimensions are discussed.
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