The subcritical accelerating Schwarzschild-Bertotti-Robinson family

Abstract

We identify the general finite-$\ell$ 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 \begin{equation*} B^2M^2=\frac{m^2}{b^2+\ell^2},\qquad AM=\frac{m\ell}{b^2+\ell^2},\qquad \frac{A}{B}=\frac{\ell}{\sqrt{b^2+\ell^2}}, \end{equation*} up to the north--south orientation convention. Thus finite real $\ell$ covers precisely the acceleration interval $|A|<|B|$: for $\ell\ne0$ 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 $\ell=0$ is the nonaccelerating Schwarzschild--BR solution, whereas $|\ell|\to\infty$ approaches the critical boundary $|A/B|=1$ from below. The Astorino parameter $\ell$ therefore parametrizes subcritical acceleration rather than an additional independent neutral black-hole degree of freedom.