Exact horizon response and charge ensembles of Majumdar--Papapetrou black holes
Abstract
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 MA and coordinate separations RAB, its entries are CAA=MA+∑B≠ AMAMB/RAB and CAB=−MAMB/RAB. 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 πn/2/Γ(n/2).
Related
- Nonlinear response and retarded three-point correlators of charge transport
- Gaussian limits for traces of circular beta-ensembles
- Diffusion Distillation for Efficient Weather Ensembles
- Spectral properties of deterministic matrices multiplied by rotationally invariant random non-Hermitian ensembles
- Bulk limits of the truncated circular beta ensembles
BibTeX
@misc{baek2026exact,
title = {{Exact horizon response and charge ensembles of Majumdar--Papapetrou black holes}},
author = {Jongheon Baek and Gihwan Nam},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23921},
eprint = {2609.23921},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23921},
}
RIS
TY - UNPB
TI - Exact horizon response and charge ensembles of Majumdar--Papapetrou black holes
AU - Jongheon Baek
AU - Gihwan Nam
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.23921
UR - https://arxiv.org/abs/2609.23921
AB - 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+∑_B≠ AM_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).
ER -