Threshold-Sharp Conformal Scalar Stability on Carter Slabs and Black Hole Exteriors

Fuente: arXiv
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Main Author: Gunara, Bobby Eka
Format: Preprint
Published: 2026
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author Gunara, Bobby Eka
author_facet Gunara, Bobby Eka
contents We prove a threshold-sharp stability theory for the conformal scalar-curvature sector on zero-curvature Carter backgrounds. The main result is a fully closed bounded-slab theorem: the reflecting evolution is constructed, the conserved energy is proved positive, the complete affine threshold obstruction is identified, and all remaining finite-energy dynamics are shown to be uniformly stable with no unstable modes. This is the sharp statement for compact reflecting slabs, where genuine time decay is false in general. We then extend the same threshold philosophy to black-hole exteriors, separating the intrinsic conformal mechanism from the exterior scalar-wave inputs needed for red-shift, local energy, limiting absorption, and zero-frequency control. The framework gives main applications to Kerr, Reissner-Nordström, slowly rotating weakly charged Kerr-Newman wall exteriors, and extremal horizon-charge obstructions. Our precise result is that it proves stability only for the conformal scalar-curvature sector, not tensorial or nonlinear gravitational stability, and it distinguishes boundedness, qualitative local decay, polynomial decay, and extremal Aretakis-type obstruction without conflating them.
format Preprint
id arxiv_https___arxiv_org_abs_2605_17400
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Threshold-Sharp Conformal Scalar Stability on Carter Slabs and Black Hole Exteriors
Gunara, Bobby Eka
Analysis of PDEs
General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
We prove a threshold-sharp stability theory for the conformal scalar-curvature sector on zero-curvature Carter backgrounds. The main result is a fully closed bounded-slab theorem: the reflecting evolution is constructed, the conserved energy is proved positive, the complete affine threshold obstruction is identified, and all remaining finite-energy dynamics are shown to be uniformly stable with no unstable modes. This is the sharp statement for compact reflecting slabs, where genuine time decay is false in general. We then extend the same threshold philosophy to black-hole exteriors, separating the intrinsic conformal mechanism from the exterior scalar-wave inputs needed for red-shift, local energy, limiting absorption, and zero-frequency control. The framework gives main applications to Kerr, Reissner-Nordström, slowly rotating weakly charged Kerr-Newman wall exteriors, and extremal horizon-charge obstructions. Our precise result is that it proves stability only for the conformal scalar-curvature sector, not tensorial or nonlinear gravitational stability, and it distinguishes boundedness, qualitative local decay, polynomial decay, and extremal Aretakis-type obstruction without conflating them.
title Threshold-Sharp Conformal Scalar Stability on Carter Slabs and Black Hole Exteriors
topic Analysis of PDEs
General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
url https://arxiv.org/abs/2605.17400