标题： 带有化学势的穿孔气体中的黑洞：玻色-爱因斯坦凝聚和熵的对数修正 显示英文标题

标题： Black holes as gases of punctures with a chemical potential: Bose-Einstein condensation and logarithmic corrections to the entropy

摘要： 我们研究当黑洞被描述为不可区分的穿孔气体时的热力学性质，带有化学势。 在这种图景中，该图景源于环量子引力，黑洞的微观状态由着色穿孔的有限半整数自旋家族定义，而由准局部静止观测者测量的近视界能量定义了各种热力学系综。 这些穿孔以面积量子的形式携带量子几何激发，总视界面积$a_\text{H}$由这些微观贡献之和给出。 我们假设系统满足玻色-爱因斯坦统计，并且每个微观状态具有全息简并度，该简并度由$\exp\big(\lambda a_\text{H}/\ell_\text{Pl}^2\big)$和$\lambda>0$给出。 我们详细分析了这些输入导致的热力学性质，并特别计算了广义规范熵。 我们解释了为什么温度固定为无畏温度且化学势为零的要求并不能完全确定大视界面积的半经典区域，并依次对各种区域进行了分类。 当简并度达到全息界限（$\lambda=1/4$）时，存在一个半经典区域，其中熵的次主导修正为对数形式。 此外，这种区域对应于玻色-爱因斯坦凝聚，在此区域内，由携带最小（或基态）自旋值$1/2$的穿孔主导。 显示英文摘要

摘要： We study the thermodynamical properties of black holes when described as gases of indistinguishable punctures with a chemical potential. In this picture, which arises from loop quantum gravity, the black hole microstates are defined by finite families of half-integers spins coloring the punctures, and the near-horizon energy measured by quasi-local stationary observers defines the various thermodynamical ensembles. The punctures carry excitations of quantum geometry in the form of quanta of area, and the total horizon area $a_\text{H}$ is given by the sum of these microscopic contributions. We assume here that the system satisfies the Bose-Einstein statistics, and that each microstate is degenerate with a holographic degeneracy given by $\exp\big(\lambda a_\text{H}/\ell_\text{Pl}^2\big)$ and $\lambda>0$. We analyze in detail the thermodynamical properties resulting from these inputs, and in particular compute the grand canonical entropy. We explain why the requirements that the temperature be fixed to the Unruh temperature and that the chemical potential vanishes do not specify completely the semi-classical regime of large horizon area, and classify in turn what the various regimes can be. When the degeneracy saturates the holographic bound ($\lambda=1/4$), there exists a semi-classical regime in which the subleading corrections to the entropy are logarithmic. Furthermore, this regime corresponds to a Bose-Einstein condensation, in the sense that it is dominated by punctures carrying the minimal (or ground state) spin value $1/2$.