标题： 带原始毛发的规范N=8超引力中的黑洞 显示英文标题

标题： Black Holes with Primary Hair in gauged N=8 Supergravity

摘要： 在本文中，我们分析了四维最大超对称规范超引力的$U(1)^{4}$约化中的静态解。 通过一种新的已知解的参数化方法，显示对于固定的电荷，根据（标量部分的）拉格朗日量的对称性破缺模式，存在三种可能的黑洞配置。 即无标量场的黑洞、具有初级标量头发的黑洞和具有次级标量头发的黑洞。 这是第一个精确的具有初级标量头发的黑洞例子，其中黑洞和标量场在视界内外都是有限的。 具有次级和初级头发的配置可以解释为作用量的离散排列和反射对称性的自发对称性破缺。 显示在热力学相空间中存在一个三重点，其中三个解共存。 讨论了相应的相变，并在无电荷情况下显式地写出了自由能作为热力学坐标函数。 在有电荷的情况下，还给出了初级头发和无头发黑洞的自由能作为热力学坐标函数。 显示英文摘要

摘要： In this paper, we analyze the static solutions for the $U(1)^{4}$ consistent truncation of the maximally supersymmetric gauged supergravity in four dimensions. Using a new parametrization of the known solutions it is shown that for fixed charges there exist three possible black hole configurations according to the pattern of symmetry breaking of the (scalars sector of the) Lagrangian. Namely a black hole without scalar fields, a black hole with a primary hair and a black hole with a secondary hair respectively. This is the first, exact, example of a black hole with a primary scalar hair, where both the black hole and the scalar fields are regular on and outside the horizon. The configurations with secondary and primary hair can be interpreted as a spontaneous symmetry breaking of discrete permutation and reflection symmetries of the action. It is shown that there exist a triple point in the thermodynamic phase space where the three solution coexist. The corresponding phase transitions are discussed and the free energies are written explicitly as function of the thermodynamic coordinates in the uncharged case. In the charged case the free energies of the primary hair and the hairless black hole are also given as functions of the thermodynamic coordinates.