标题： 修正引力理论中的黑洞解 显示英文标题

标题： Black hole solutions of modified gravity theories

摘要： 本文探讨了比广义相对论更为普遍框架下的毛发黑洞，考虑了宇宙常数、高维空间、异乎寻常的物质场或更高曲率项的存在。 这些对广义相对论的扩展可以在弦理论的背景下推导出来。 通过研究自然的广义相对论扩展，我们也能更深入地理解爱因斯坦的理论。 首先，我们将展示广义相对论及其构建模块，特别是随后需要的数学工具。 然后，我们将详细介绍一个扩展，引入高维空间和p形式场，它们构成了电磁相互作用的自然推广。 在这个框架下，我们将构建新的静态黑洞解，其中p形式场允许塑造视界的几何形状。 其次，我们将介绍爱因斯坦理论在任意维度上的通用扩展，这会产生二阶场方程：Lovelock理论。 在此背景下，我们将确定一类六维解，其中该理论简化为存在p形式场的爱因斯坦-高斯-博内理论。 第三，我们将研究四维广义相对论的扩展，其修改由共形耦合标量场诱导。 我们将展示一个具有平坦视界的新型黑洞解，在轴子场存在的情况下。 为了结束本论文，我们将研究这些引力理论的热力学方面。 这样，我们将能够确定这些新解的质量和电荷，并检查共形标量场存在时的相变现象。 显示英文摘要

摘要： The main interest of the work exposed in this thesis is to explore hairy black holes in a more general framework than General Relativity by taking into account the presence of a cosmological constant, of higher dimensions, of exotic matter fields or of higher curvature terms. These extensions to General Relativity can be derived in the context of String Theory. It is also by studying natural extensions to General Relativity that we can more deeply understand the theory of Einstein. Firstly, we will display the theory of General Relativity with its building blocks in particular and we will give the mathematical tools that we need afterwards. Then, a first extension will be detailed with the introduction of higher dimensions and p-form fields which constitute the natural generalization of the electromagnetic interaction. We will build in this framework new static black hole solutions where p-form fields allow to shape the geometry of the horizon. Secondly, we will present the general extension of Einstein theory in any dimension which produces second order field equations: Lovelock theory. We will determine in this context a large class of solutions in dimension 6 for which the theory is reduced to Einstein-Gauss-Bonnet theory with the presence of p-form fields. Thirdly, we will study a generalization of General Relativity in dimension 4 whose modification is induced by a conformally coupled scalar field. We will namely exhibit a new black hole solution with a flat horizon in the presence of axionic fields. To conclude this thesis, thermodynamical aspects of these gravitational theories will be studied. In this way, we will be able to determine the mass and the charges of these new solutions and we will examine phase transition phenomena in the presence of a conformally scalar field.