Continuum Landscape of stable extra-dimensional metrics
Abstract
We investigate modified gravity with quadratic curvature terms (R2, RABRAB, and RABCDRABCD). In this framework, the geometry of the extra dimensions is determined by the higher-dimensional field equations together with auxiliary conditions. For inhomogeneous metrics, we derive new stability conditions under radion excitations. The central result is that stable solutions satisfying these conditions are not isolated: a typical stable regular metric belongs to a continuous family of stable metrics in its immediate neighbourhood. Since the effective four-dimensional physical parameters depend on the extra-dimensional geometry, this geometrical landscape of stable metrics induces a continuous landscape of effective four-dimensional parameters. Transitions between distinct static solutions within the landscape cannot be induced by spatially localized perturbations, whose asymptotic decay (|x|→∞) preserves the boundary data distinguishing the states. We also note a possible topological transition from a two-brane to a one-brane configuration, associated with a change in the number of regular zeros of the metric function r(u).
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BibTeX
@misc{rubin2026continuum,
title = {{Continuum Landscape of stable extra-dimensional metrics}},
author = {Sergey G. Rubin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08006},
eprint = {2610.08006},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08006},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Continuum Landscape of stable extra-dimensional metrics
AU - Sergey G. Rubin
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08006
UR - https://arxiv.org/abs/2610.08006
AB - We investigate modified gravity with quadratic curvature terms (R^2, R_ABR^AB, and R_ABCDR^ABCD). In this framework, the geometry of the extra dimensions is determined by the higher-dimensional field equations together with auxiliary conditions. For inhomogeneous metrics, we derive new stability conditions under radion excitations. The central result is that stable solutions satisfying these conditions are not isolated: a typical stable regular metric belongs to a continuous family of stable metrics in its immediate neighbourhood. Since the effective four-dimensional physical parameters depend on the extra-dimensional geometry, this geometrical landscape of stable metrics induces a continuous landscape of effective four-dimensional parameters. Transitions between distinct static solutions within the landscape cannot be induced by spatially localized perturbations, whose asymptotic decay (|x|→∞) preserves the boundary data distinguishing the states. We also note a possible topological transition from a two-brane to a one-brane configuration, associated with a change in the number of regular zeros of the metric function r(u).
ER -