Local obstructions to trapped-region escape in modified gravity
Abstract
Energy conditions in modified gravity are commonly imposed on an ''effective'' stress tensor that mixes physical matter with additional gravitational degrees of freedom, obscuring which sector actually controls null focusing, horizon multiplicity, and the disappearance of trapped regions. We develop a geometry-first alternative in spherical symmetry. For a normalized pair of future-directed radial null vectors, twolongitudinal Ricci projections and one independent transverse Einstein projection obey exact area-weighted transport laws. These imply a trapping-persistence theorem: after a nondegenerate future-outer marginal sphere, a regular ingoing generator cannot exit the trapped region while the ingoing longitudinal and transverse convergence channels remain nonnegative. In metric f(R) gravity, with F≡ df/dR>0, we then construct an entropy-resolved hierarchy based on the local Wald-density variable Fr2. In the longitudinal entropy-focusing law, the scalaron second derivative cancels exactly, leaving a nonpositive scalar-gradient square together with the physical matter projection; in the independent transverse entropy-transport law, all scalaron derivative terms cancel. Entropy trapping is consequently governed by the physical matter condition Tnn≥ 0 and an algebraic mixed threshold rather than by a fictitious effective fluid. The resulting hierarchy cleanly separates matter positivity, geometric focusing, marginal-surface recovery, and gravitational-entropy evolution, and identifies the precise local reversals required for regular inner horizons, throats, and trapped-to-antitrapped transitions.
Versions
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BibTeX
@misc{lobo2026local,
title = {{Local obstructions to trapped-region escape in modified gravity}},
author = {Francisco S. N. Lobo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27225},
eprint = {2610.27225},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27225},
}
RIS
TY - UNPB
TI - Local obstructions to trapped-region escape in modified gravity
AU - Francisco S. N. Lobo
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27225
UR - https://arxiv.org/abs/2610.27225
AB - Energy conditions in modified gravity are commonly imposed on an ''effective'' stress tensor that mixes physical matter with additional gravitational degrees of freedom, obscuring which sector actually controls null focusing, horizon multiplicity, and the disappearance of trapped regions. We develop a geometry-first alternative in spherical symmetry. For a normalized pair of future-directed radial null vectors, twolongitudinal Ricci projections and one independent transverse Einstein projection obey exact area-weighted transport laws. These imply a trapping-persistence theorem: after a nondegenerate future-outer marginal sphere, a regular ingoing generator cannot exit the trapped region while the ingoing longitudinal and transverse convergence channels remain nonnegative. In metric f(R) gravity, with F≡ df/dR>0, we then construct an entropy-resolved hierarchy based on the local Wald-density variable Fr^2. In the longitudinal entropy-focusing law, the scalaron second derivative cancels exactly, leaving a nonpositive scalar-gradient square together with the physical matter projection; in the independent transverse entropy-transport law, all scalaron derivative terms cancel. Entropy trapping is consequently governed by the physical matter condition T_nn≥ 0 and an algebraic mixed threshold rather than by a fictitious effective fluid. The resulting hierarchy cleanly separates matter positivity, geometric focusing, marginal-surface recovery, and gravitational-entropy evolution, and identifies the precise local reversals required for regular inner horizons, throats, and trapped-to-antitrapped transitions.
ER -