Dilatonic Reissner--Nordström black holes in a Bertotti--Robinson magnetic background
Abstract
We construct an exact static, magnetically charged solution of four-dimensional Einstein--Maxwell--dilaton theory that generalizes the centered Reissner--Nordström black hole in a Bertotti--Robinson magnetic background. Its pure-background limit is the magnetic EMD deformation of Bertotti--Robinson spacetime. Using the Emparan--Teo solution-generating technique, the charged construction reduces in canonical Weyl coordinates to replacing the Schwarzschild horizon rod by the Reissner--Nordström rod of half-length σ=√(m2−e2) and integrating the resulting nonlinear background--rod interaction. This yields a completely explicit solution for arbitrary dilaton coupling α, with the expected special limits and numerical verification of the full field equations. The horizon exhibits a coupled mechanical, electromagnetic and intrinsic response to the monopole--background interaction. The residual conical stress is tied to north--south magnetic polarization; increasing the background field produces the ordered reversal scales Bpole<Bcrit<Beq, independent of α at fixed seed parameters (m,e), while Gauss--Bonnet identifies the conical stress with the integrated distributional Gaussian-curvature contribution at the singular pole. Along the fixed-$(m,B,α,C)$ near-extremal path considered here, every α>0 gives vanishing horizon area and divergent curvature, whereas a correlated near-extremal strong-field limit yields a universal magnetic-reversal law.
Related
- Reissner-Nordstrom in the Bertotti-Robinson-Bonnor-Melvin electromagnetic field
- On the Extended Kerr-Newman-Bertotti-Robinson Spacetime: Two Black Holes and a Naked Singularity in Bertotti-Robinson Universe
- From Bertotti–Robinson to vacuum: New exact solutions in general relativity via Harrison and Inversion symmetries
- Dynamics, ringdown, and accretion-driven multiple quasi-periodic oscillations of Kerr–Bertotti–Robinson black holes
- Nonoscillatory gravitational quasinormal modes of Reissner–Nordström–de Sitter spacetime
BibTeX
@misc{hong2026dilatonic,
title = {{Dilatonic Reissner--Nordström black holes in a Bertotti--Robinson magnetic background}},
author = {Kenneth Hong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31408},
eprint = {2609.31408},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31408},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dilatonic Reissner--Nordström black holes in a Bertotti--Robinson magnetic background
AU - Kenneth Hong
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31408
UR - https://arxiv.org/abs/2609.31408
AB - We construct an exact static, magnetically charged solution of four-dimensional Einstein--Maxwell--dilaton theory that generalizes the centered Reissner--Nordström black hole in a Bertotti--Robinson magnetic background. Its pure-background limit is the magnetic EMD deformation of Bertotti--Robinson spacetime. Using the Emparan--Teo solution-generating technique, the charged construction reduces in canonical Weyl coordinates to replacing the Schwarzschild horizon rod by the Reissner--Nordström rod of half-length σ=√(m^2−e^2) and integrating the resulting nonlinear background--rod interaction. This yields a completely explicit solution for arbitrary dilaton coupling α, with the expected special limits and numerical verification of the full field equations. The horizon exhibits a coupled mechanical, electromagnetic and intrinsic response to the monopole--background interaction. The residual conical stress is tied to north--south magnetic polarization; increasing the background field produces the ordered reversal scales B_pole<B_crit<B_eq, independent of α at fixed seed parameters (m,e), while Gauss--Bonnet identifies the conical stress with the integrated distributional Gaussian-curvature contribution at the singular pole. Along the fixed-$(m,B,α,C)$ near-extremal path considered here, every α>0 gives vanishing horizon area and divergent curvature, whereas a correlated near-extremal strong-field limit yields a universal magnetic-reversal law.
ER -