AI 中文总结
研究非极端RN黑洞近地平线区域的弦卡罗尔展开在接近极端极限时的行为，发现其虽能捕捉非极端近地平线林德勒区域，但不足以恢复极端$AdS_2×S^2$喉道，通过特定坐标下的二阶展开等方法得到极端喉道几何。
AI 中文摘要
非极端黑洞的近地平线区域具有通用的林德勒形式，但严格的视界极限不是普通的洛伦兹几何。在这种非极端近地平线度规的弦卡罗尔展开中，横向角方向构成基底，时间 - 径向林德勒方向作为在该基顶上纤维化的一个特殊二维纵向扇区出现。我们研究当接近极端极限时，对于雷斯纳 - 诺德斯特龙（RN）黑洞，这种弦卡罗尔展开的行为，预期的近地平线几何是洛伦兹$AdS_2×S^2$喉道。我们表明，对于四维非极端RN几何，弦卡罗尔展开能正确捕捉近地平线林德勒区域，但不足以恢复极端$AdS_2×S^2$喉道。原因是在弦卡罗尔展开中被抑制的高阶项在极端极限中变得至关重要。我们表明在爱丁顿 - 芬克尔斯坦坐标中，所需贡献出现在二阶并恢复了$AdS_2$几何所需的径向依赖性。然后通过缩放喉道几何的零温度极限得到极端$AdS_2×S^2$喉道。在静态坐标中，极端喉道几何的时间扇区可从二阶近地平线展开获得，但径向扇区不能从任何有限阶截断获得，需要近地平线展开中所有阶的贡献。
英文摘要
The near horizon region of a non extremal black hole has a universal Rindler form, but the strict horizon limit is not an ordinary Lorentzian geometry. In the String Carroll expansion of this non extremal near horizon metric,the transverse angular directions form a base and the time-radial Rindler directions appear as a distinguished two-dimensional longitudinal sector fibered over this base. We study how this String Carroll expansion behaves for the Reissner-Nordström (RN) black hole as the extremal limit is approached, where the expected near horizon geometry is the Lorentzian $AdS_2 \times S^2$ throat. We show that while for the four-dimensional non extremal RN geometry, the String Carroll expansion correctly captures the near horizon Rindler region, it is not sufficient to recover the extremal $AdS_2 \times S^2$ throat. The reason is that the higher order terms, which are suppressed in the String Carroll expansion, become essential in the extremal limit. We show that in Eddington-Finkelstein coordinates, the required contribution appears at second order and restores the radial dependence needed for the $AdS_2$ geometry. The extremal $AdS_2 \times S^2$ throat is then obtained as the zero-temperature limit of the scaled throat geometry. In static coordinates, the temporal sector of the extremal throat geometry can be obtained from a second order near horizon expansion, but the radial sector cannot be obtained from any finite order truncation and requires contributions from all orders in the near horizon expansion.
Comments23 pages
