发表机构
Institute for Basic Science (IBS); Ben-Gurion University of the Negev; Frankfurt Institute for Advanced Studies (FIAS); Bahamas Advanced Study Institute and Conferences（基础科学研究所; 内盖夫本-古里安大学; 法兰克福高等研究院; 巴哈马高级研究学院与会议）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在修正测度弦框架下，通过径向张力刺猬构造，提出模型无关条件，实现满足零能量条件的渐近平坦规则黑洞，其首个史瓦西修正出现在$r^{-4}$阶。
AI 中文摘要
具有非零恒定张力的径向弦球状云，其能量密度正比于$r^{-2}$，因此产生奇异锥形几何而非渐近平坦的规则黑洞。我们证明，在修正测度弦公式中，这一障碍可以被消除。由复合体张力标量生成的径向世界片连续统，在受约束的$\mathrm{SO}(3)$刺猬分支上，约化为爱因斯坦引力与非线性函数$K(Y)$及辅助三形式场的耦合。该构造直接以径向张力$\mathcal{T}(r)$给出模型无关的条件。中心处有限曲率要求$\mathcal{T}=\mathcal{O}(r^2)$，而零能量条件禁止更快的首阶幂次。因此，满足零能量条件的正规则中心必然是德西特时空。有限ADM质量要求张力在无穷远处被屏蔽，而主能量条件对于以快于$r^{-2}$屏蔽的非平凡正分布无法全局成立。一个精确的三次方分布实现了这些性质，并给出一个渐近平坦几何规则黑洞的连续族，其对史瓦西解的首个修正出现在$r^{-4}$阶。
英文摘要
A spherical cloud of radial strings with non-zero constant tension has an energy density proportional to $r^{-2}$ and therefore produces a singular conical geometry rather than an asymptotically flat regular black hole. We show that this obstruction can be removed within the modified-measure formulation of strings. A continuum of radial worldsheets whose tensions are generated by a composite bulk tension scalar reduces, on a constrained $\mathrm{SO}(3)$ hedgehog branch, to Einstein gravity coupled to a nonlinear function $K(Y)$ and an auxiliary three-form. This construction gives model-independent conditions directly in terms of the radial tension $\mathcal{T}(r)$. Finite curvature at the centre requires $\mathcal{T}=\mathcal{O}(r^2)$, while the null energy condition forbids a faster leading power. Thus a positive regular centre satisfying the null energy condition is necessarily de Sitter. Finite ADM mass requires the tension to be screened at infinity, whereas the dominant energy condition cannot hold globally for a non-trivial positive profile screened faster than $r^{-2}$. An exact cubic profile realises these properties and gives a continuous family of asymptotically flat geometrically regular black holes whose first correction to Schwarzschild appears at order $r^{-4}$.
Comments5 pages, 1 figure
