The Quantum Boundary of Black Hole Interiors: Signature Failure and the Termination of Mass Inflation

Abstract

Classical general relativity predicts a singularity at the center of every black hole. We argue that it is never reached. We adopt the conjecture of Shaya (2026) that a metric element of non-Lorentzian signature is inadmissible: it cannot enter the Feynman sum over geometries, and so cannot belong to the physical manifold. Nothing beyond standard quantum mechanics is invoked. Signature is the only pointwise diffeomorphism-invariant content of the metric, so the criterion is local and coordinate independent. Transverse-traceless graviton vacuum fluctuations grow as ${\Delta }_g=\sqrt{8/\pi }{\ell }_P/q$ on a scale $q$, and any finite-scale metric stress driving an eigenvalue through zero removes that element. When the surviving elements can no longer sustain connected, differentiable, causally propagating support, the manifold terminates on a quantum boundary ${\mathcal{B}}_Q$ at finite radius. For the vacuum Schwarzschild interior the tidal Weyl stress gives $r_{\mathrm{qb}}\simeq 1.0\times 10^{-22}(M/M_{\odot }{)}^{1/3}$~m for the adopted curvature response $C_W=0.15$. For a spinning hole, the boundary forms much farther out: mass inflation at the inner horizon $r_{-}$ concentrates an exponentially growing interior mass into a thin layer whose thickness is set by the accretion rate and floored at one spatial quantum, and the counter-streaming null fluxes supply a trace-free Ricci stress along the radial axis alone. This caps the factor $n_{\mathrm{qb}}$ by which mass inflation can amplify the interior mass function, at between $10^{38}$ and $10^{69}$ for a $10M_{\odot }$ hole depending on its accretion history, and leaves the Cauchy horizon, the ring, and all deeper extensions outside the physical manifold. The Gibbons--Hawking--York term over this terminal slice yields a finite interior action, $S_{GHY}^{qb}\approx \frac{3}{2}{n}_{\mathrm{qb}}M{c}^2\Delta t$.

17 pages, no figures: Substantial changes. Cause of Quantum Boundary at singularities is due to quantum fluctuations plus metric stress changing signature of metrics to nonLorentzian and therefore inadmissable to Feynman-DeWitt sum of geometries