Closure of Traceful Radiation-Gauge Reconstruction with Matter: General Kerr Conditions, a Thin-Shell Benchmark, and a Conserved Torus
Abstract
We formulate the closure problem for first-order, traceful radiation-gauge metric reconstruction on a Kerr background with matter. The reconstruction is decomposed into Weyl-curvature, Ricci-trace, and mass--angular-momentum completion sectors. For compatible initial, gauge, and completion data, we establish local existence and uniqueness of the resulting triangular transport system on a regular Kerr domain, and identify the additional conditions needed for a closed global formulation. This is not a global existence theorem. We test the framework using two conserved matter sources. For a thin shell around a Schwarzschild black hole, Israel matching, regularity, asymptotic flatness, a barotropic equation of state, and fixed rest mass determine the static, axial, and leading rotational sectors. The ADM-mass shift is √(1−2M/R) times the shell rest mass, while the axial sector determines the angular momentum, moment of inertia, and interior frame dragging. We also construct a stationary constant-angular-momentum fluid torus on Kerr and compute its Newman--Penrose Ricci projections, showing that nonspherical sources generally excite coupled Ricci sectors. The shell provides a closed benchmark, while the torus illustrates the additional structure required for general Kerr sources.
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BibTeX
@misc{nashed2026closure,
title = {{Closure of Traceful Radiation-Gauge Reconstruction with Matter: General Kerr Conditions, a Thin-Shell Benchmark, and a Conserved Torus}},
author = {G. G. L. Nashed},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35938},
eprint = {2610.35938},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35938},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Closure of Traceful Radiation-Gauge Reconstruction with Matter: General Kerr Conditions, a Thin-Shell Benchmark, and a Conserved Torus
AU - G. G. L. Nashed
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.35938
UR - https://arxiv.org/abs/2610.35938
AB - We formulate the closure problem for first-order, traceful radiation-gauge metric reconstruction on a Kerr background with matter. The reconstruction is decomposed into Weyl-curvature, Ricci-trace, and mass--angular-momentum completion sectors. For compatible initial, gauge, and completion data, we establish local existence and uniqueness of the resulting triangular transport system on a regular Kerr domain, and identify the additional conditions needed for a closed global formulation. This is not a global existence theorem. We test the framework using two conserved matter sources. For a thin shell around a Schwarzschild black hole, Israel matching, regularity, asymptotic flatness, a barotropic equation of state, and fixed rest mass determine the static, axial, and leading rotational sectors. The ADM-mass shift is √(1−2M/R) times the shell rest mass, while the axial sector determines the angular momentum, moment of inertia, and interior frame dragging. We also construct a stationary constant-angular-momentum fluid torus on Kerr and compute its Newman--Penrose Ricci projections, showing that nonspherical sources generally excite coupled Ricci sectors. The shell provides a closed benchmark, while the torus illustrates the additional structure required for general Kerr sources.
ER -