Majumdar--Papapetrou黑洞的精确视界响应与电荷系综
Exact horizon response and charge ensembles of Majumdar--Papapetrou black holes
浏览论文内容
中文总结 AI 辅助
本文推导了四维及高维Majumdar--Papapetrou时空的精确电容矩阵与格林函数，揭示了视界间电荷转移和自能修正，并推广至任意维数。
中文摘要 AI 辅助
我们确定了任意四维Majumdar--Papapetrou时空的静电Dirichlet-to-Neumann映射。对于最小耦合的旁观者Maxwell场，不相连的极端视界的势可以独立指定，由此产生的通量电荷由一个精确的电容矩阵关联。若中心具有质量$M_A$和坐标间距$R_{AB}$，其矩阵元为$C_{AA}=M_A+\sum_{B\ne A}M_AM_B/R_{AB}$和$C_{AB}=-M_AM_B/R_{AB}$。该矩阵是一个正对角项加上视界完全图的加权拉普拉斯算子，从而给出场能量的精确共模和差模分解。接地Dirichlet格林函数表明，点电荷根据基本调和测度将其通量在无穷远和视界之间分配。Frolov和Zelnikov的多中心格林函数的直接翻译给出了他们发表的式(68)中使用的对角补全，其分量分解的Gauss通量保持总视界电荷，但通常在视界之间转移电荷。而保持每个视界电荷的对称格林函数则包含完整电容矩阵的逆。对于双黑洞，两者之差给出一个有限的、负半定的静电自能平移，以及相应的精确自力差，无需额外的紫外减除。最后，我们将响应矩阵、通量分配和固定电荷格林函数推广到$D=n+3$维，其中图权重获得普适因子$\pi^{n/2}/\Gamma(n/2)$。
英文摘要
We determine the electrostatic Dirichlet-to-Neumann map of an arbitrary four-dimensional Majumdar--Papapetrou spacetime. For a minimally coupled spectator Maxwell field, the potentials of the disconnected extremal horizons may be prescribed independently, and the resulting flux charges are related by an exact capacitance matrix. If the centers have masses $M_A$ and coordinate separations $R_{AB}$, its entries are $C_{AA}=M_A+\sum_{B\ne A}M_AM_B/R_{AB}$ and $C_{AB}=-M_AM_B/R_{AB}$. The matrix is a positive diagonal term plus the weighted Laplacian of the complete graph of horizons, giving an exact common-mode and differential-mode decomposition of the field energy. The grounded Dirichlet Green function shows that a point charge partitions its flux among infinity and the horizons according to elementary harmonic measures. A direct translation of the multicenter Green function of Frolov and Zelnikov gives the diagonal completion used in their published Eq.~(68), whose component-resolved Gauss flux preserves the total horizon charge but generally transfers charge between horizons. The symmetric Green function that preserves every horizon charge instead contains the inverse of the full capacitance matrix. For a binary, the difference gives a finite, negative-semidefinite shift of the electrostatic self-energy and a corresponding exact self-force difference without an additional ultraviolet subtraction. We finally extend the response matrix, flux partition, and fixed-charge Green function to $D=n+3$ dimensions, where the graph weights acquire the universal factor $π^{n/2}/Γ(n/2)$.
发表机构
- Yonsei University（延世大学）
机构由 AI 辅助整理，请以论文原文为准。
