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 Δg = √(8/π) ℓP/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 ℬQ at finite radius. For the vacuum Schwarzschild interior the tidal Weyl stress gives rqb ≃ 1.0×10−22(M/M⊙)1/3~m for the adopted curvature response CW=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 nqb by which mass inflation can amplify the interior mass function, at between 1038 and 1069 for a 10 M⊙ 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, SGHYqb ≈ 3/2 nqb Mc2 Δt.
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BibTeX
@misc{shaya2026quantum,
title = {{The Quantum Boundary of Black Hole Interiors: Signature Failure and the Termination of Mass Inflation}},
author = {Edward J. Shaya},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.15423},
eprint = {2606.15423},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.15423},
}
RIS
TY - UNPB
TI - The Quantum Boundary of Black Hole Interiors: Signature Failure and the Termination of Mass Inflation
AU - Edward J. Shaya
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2606.15423
UR - https://arxiv.org/abs/2606.15423
AB - 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 Δ_g = √(8/π) ℓ_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 ℬ_Q at finite radius. For the vacuum Schwarzschild interior the tidal Weyl stress gives r_qb ≃ 1.0×10^−22(M/M_⊙)^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_qb by which mass inflation can amplify the interior mass function, at between 10^38 and 10^69 for a 10 M_⊙ 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 ≈ 3/2 n_qb Mc^2 Δt.
ER -