Frozen-In Gravitational Fields
Abstract
Spacetime can undergo complex nonlinear evolution, as governed by the Einstein field equations, and a central challenge is to understand the geometric structures that arise, persist, and interact throughout its evolution. Using a formulation of Einstein equations that parallels nonlinear electrodynamics of continuous media, we show that general relativity admits gravitational field connections---two-surfaces and associated field lines whose connectivity is maintained by the spacetime dynamics. This gravitational frozen-in behavior is enabled by an ideal Ohm-type condition for the gravitational field. We further show that the same framework naturally leads to a conserved ``gravitational magnetic'' flux. A conserved gravitational helicity also emerges, with a clear topological interpretation in terms of gravitational field-line structures. These results identify well-defined topological constraints on admissible spacetime evolution and provide an organizing principle underlying the nonlinear dynamics of spacetime.
Versions
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BibTeX
@misc{asenjo2026frozenin,
title = {{Frozen-In Gravitational Fields}},
author = {Felipe A. Asenjo and Maricarmen A. Winkler and Luca Comisso},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25240},
eprint = {2609.25240},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25240},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Frozen-In Gravitational Fields
AU - Felipe A. Asenjo
AU - Maricarmen A. Winkler
AU - Luca Comisso
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25240
UR - https://arxiv.org/abs/2609.25240
AB - Spacetime can undergo complex nonlinear evolution, as governed by the Einstein field equations, and a central challenge is to understand the geometric structures that arise, persist, and interact throughout its evolution. Using a formulation of Einstein equations that parallels nonlinear electrodynamics of continuous media, we show that general relativity admits gravitational field connections---two-surfaces and associated field lines whose connectivity is maintained by the spacetime dynamics. This gravitational frozen-in behavior is enabled by an ideal Ohm-type condition for the gravitational field. We further show that the same framework naturally leads to a conserved ``gravitational magnetic'' flux. A conserved gravitational helicity also emerges, with a clear topological interpretation in terms of gravitational field-line structures. These results identify well-defined topological constraints on admissible spacetime evolution and provide an organizing principle underlying the nonlinear dynamics of spacetime.
ER -