Intrinsic spatial-strain shortcuts in general relativity
Abstract
We analyze spacetime shortcuts generated by longitudinal contraction and transverse expansion of the intrinsic spatial metric at fixed reference volume. Smooth bounded ultrastatic corridors are globally hyperbolic and geodesically complete and produce an exact travel-time advance between exterior clocks. An axial maximum makes the axial light ray globally minimizing; a strict maximum on an interior interval establishes Olum's endpoint-surface criterion for exactly matched corridors. Exact Einstein-source identities distinguish integrated Eulerian matter energy from asymptotic mass: infinite tubes have negative integrated energy, whereas finite corridors admit competing gradient contributions. A transverse Ricci identity proves local null-energy violation in every nontrivial localized finite corridor. The axial averaged null energy is strictly negative for localized axial-maximum profiles, and quantitative bounds relate its magnitude to the reference time advance and peak strain. We also obtain the complete finite-profile Ricci spectrum and the axial passenger tidal tensor. These results provide explicit causal and source constraints on a prepared geometry without specifying its physical formation or matter dynamics.
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BibTeX
@misc{lobo2026intrinsic,
title = {{Intrinsic spatial-strain shortcuts in general relativity}},
author = {Francisco S. N. Lobo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09143},
eprint = {2610.09143},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09143},
}
RIS
TY - UNPB
TI - Intrinsic spatial-strain shortcuts in general relativity
AU - Francisco S. N. Lobo
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.09143
UR - https://arxiv.org/abs/2610.09143
AB - We analyze spacetime shortcuts generated by longitudinal contraction and transverse expansion of the intrinsic spatial metric at fixed reference volume. Smooth bounded ultrastatic corridors are globally hyperbolic and geodesically complete and produce an exact travel-time advance between exterior clocks. An axial maximum makes the axial light ray globally minimizing; a strict maximum on an interior interval establishes Olum's endpoint-surface criterion for exactly matched corridors. Exact Einstein-source identities distinguish integrated Eulerian matter energy from asymptotic mass: infinite tubes have negative integrated energy, whereas finite corridors admit competing gradient contributions. A transverse Ricci identity proves local null-energy violation in every nontrivial localized finite corridor. The axial averaged null energy is strictly negative for localized axial-maximum profiles, and quantitative bounds relate its magnitude to the reference time advance and peak strain. We also obtain the complete finite-profile Ricci spectrum and the axial passenger tidal tensor. These results provide explicit causal and source constraints on a prepared geometry without specifying its physical formation or matter dynamics.
ER -