非多项式引力中的有理正则黑洞
Rational regular black holes in non-polynomial gravity
- Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学物理学院理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究d≥4维非多项式纯引力理论，构造无需无穷多修正项的正则黑洞解，证明带电时可抑制质量通胀，拟正则黑洞可解决库仑奇点问题。
AI中文摘要：
我们研究d≥4维的非多项式纯引力理论，这类理论在球对称下约化到二维时，会在小尺度上对广义相对论的二维约化进行最小修正。它们满足伯克霍夫定理，且对于任意耦合参数都存在精确黑洞解。这些解的熵带有对数主导修正，牛顿势带有类量子修正，二者均源自正则化的临界阶d=2p理论，在偶数维中该理论与二维轨道空间的欧拉示性数相关。这类黑洞可通过任意阶p>d/2的不变量实现正则化，无需无穷多修正项；在偶数维中，其光滑性随修正项数量线性变化，且无需精细调节。我们构造了一类理论，其唯一（无质量）真空为（反）德西特时空[(A)dS₄]或闵可夫斯基时空(M₄)的极值黑洞形变，熵为零，从而满足热力学能斯特第三定律且熵无间断。我们证明麦克斯韦场不会破坏度规的正则性，作用量中简单的非最小耦合可使电场正则化。考虑无穷多修正项时，我们构造了单视界的拟正则黑洞，以及对任意质量均具有近极值内视界的正则（反）德西特核心黑洞。带电时，这两类黑洞可阻止或抑制质量通货膨胀，条件为质量M与电荷Q满足形式为M>αℓ+βQ²/ℓ的不等式，其中α、β为依赖于具体模型的数值因子，ℓ为控制高能修正的长度尺度。拟正则黑洞足以解决库仑奇点问题，无需非最小耦合。
英文摘要：
We consider the $d\geq 4$ non-polynomial pure gravity theories defined so that their 2D reduction to spherical symmetry minimally modifies that of General Relativity at small distances. They satisfy Birkhoff theorem and admit exact black hole solutions for an arbitrary number of couplings. These solutions have a logarithmic leading correction to the entropy and a quantum-like correction to the Newtonian potential, both arising from the regularised critical order $d=2p$ theory, which is related in even dimensions to the Euler characteristic of the 2D orbit space. These black holes can be made regular, without the need for infinite towers of corrections, using invariants of any order $p>d/2$. In even dimensions, their smoothness is linear in the number of corrections and does not require fine-tuning. We construct a class of theories admitting as unique (massless) vacuum an extremal black hole deformation of (A)dS$_4$ or M$_4$ with vanishing entropy, so that Nernst's third law of thermodynamics is satisfied without discontinuity in the entropy. We show that a Maxwell field does not disrupt the regularity of the metric, and that simple non-minimal couplings in the action enable to regularise the electric field. Considering infinite towers of corrections, we construct quasi-regular black holes with one horizon as well as regular (A)dS-core ones with a near-extremal inner horizon for any mass. When charged, these two types of black holes prevent or tame the mass inflation provided the mass and charge satisfy an inequality of the form $M > α\ell + βQ^2 / \ell$, where $α$ and $β$ are numerical factors depending on the specific model, while $\ell$ is the length scale controlling the high-energy corrections. The quasi-regular black holes are sufficient to resolve the Coulomb singularity without the need for non-minimal couplings.
