The subcritical accelerating Schwarzschild-Bertotti-Robinson family
Abstract
We identify the general finite-ℓ neutral Alekseev--Astorino Schwarzschild--Bertotti--Robinson family with the subcritical branch of the independently obtained accelerating Schwarzschild--Bertotti--Robinson solution. The exact scale-free dictionary is B2M2=m2/(b2+ℓ2), AM=mℓ/(b2+ℓ2), A/B=ℓ/(√(b2+ℓ2)), up to the north--south orientation convention. Thus finite real ℓ covers precisely the acceleration interval |A|<|B|: for ℓ≠0 the corresponding OP acceleration parameter is nonzero and the two axial openings are unequal, although no acceleration horizon is present. We establish the identification by canonical Weyl-rod matching and horizon-shape comparison, an independent conicity check, and an exact off-horizon reconstruction of the metric and Maxwell field. The centered limit ℓ=0 is the nonaccelerating Schwarzschild--BR solution, whereas |ℓ|→∞ approaches the critical boundary |A/B|=1 from below. The Astorino parameter ℓ therefore parametrizes subcritical acceleration rather than an additional independent neutral black-hole degree of freedom.
Related
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BibTeX
@misc{hong2026subcritical,
title = {{The subcritical accelerating Schwarzschild-Bertotti-Robinson family}},
author = {Kenneth Hong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31035},
eprint = {2610.31035},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31035},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The subcritical accelerating Schwarzschild-Bertotti-Robinson family
AU - Kenneth Hong
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31035
UR - https://arxiv.org/abs/2610.31035
AB - We identify the general finite-ℓ neutral Alekseev--Astorino Schwarzschild--Bertotti--Robinson family with the subcritical branch of the independently obtained accelerating Schwarzschild--Bertotti--Robinson solution. The exact scale-free dictionary is B^2M^2=m^2/(b^2+ℓ^2), AM=mℓ/(b^2+ℓ^2), A/B=ℓ/(√(b^2+ℓ^2)), up to the north--south orientation convention. Thus finite real ℓ covers precisely the acceleration interval |A|<|B|: for ℓ≠0 the corresponding OP acceleration parameter is nonzero and the two axial openings are unequal, although no acceleration horizon is present. We establish the identification by canonical Weyl-rod matching and horizon-shape comparison, an independent conicity check, and an exact off-horizon reconstruction of the metric and Maxwell field. The centered limit ℓ=0 is the nonaccelerating Schwarzschild--BR solution, whereas |ℓ|→∞ approaches the critical boundary |A/B|=1 from below. The Astorino parameter ℓ therefore parametrizes subcritical acceleration rather than an additional independent neutral black-hole degree of freedom.
ER -