A Geometric No-Go Theorem for Regular Black Holes in Scalar-Tensor Theories
Abstract
Perturbative instabilities generically puzzles singularity-free spacetimes, including non-singular bounce, traversible wormholes and regular black holes (RBHs). Can the scalar-tensor (ST) theories that stabilize the first two also stabilize RBHs? We show that the answer is no for static, spherically symmetric RBHs supported by a radial scalar field within a broad class of ST theories. In any RBHs with two-horizon structure, the ratio of the longitudinal scale to the sphere radius must attain an interior maximum. The proper-time derivative of that ratio is associated to the squared propagation speed of odd-parity tensor perturbations by the background field equations in a broad class of scalar-tensor theories. A Lorentzian odd-tensor cone then requires a local minimum instead of a maximum. This conflicts indicate a geometric no-go theorem, covering a broad class of ST theories including spatially covariant gravity, Horndeski theory, quadratic GLPV, DHOST, and U-DHOST theories, and their admissible disformal extensions. Viable RBHs therefore require relaxing at least one geometric or dynamical assumption.
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BibTeX
@misc{peng2026geometric,
title = {{A Geometric No-Go Theorem for Regular Black Holes in Scalar-Tensor Theories}},
author = {Shulang Peng and Jun Tao and Mian Zhu and Yi-Fu Cai},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06460},
eprint = {2611.06460},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06460},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Geometric No-Go Theorem for Regular Black Holes in Scalar-Tensor Theories
AU - Shulang Peng
AU - Jun Tao
AU - Mian Zhu
AU - Yi-Fu Cai
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06460
UR - https://arxiv.org/abs/2611.06460
AB - Perturbative instabilities generically puzzles singularity-free spacetimes, including non-singular bounce, traversible wormholes and regular black holes (RBHs). Can the scalar-tensor (ST) theories that stabilize the first two also stabilize RBHs? We show that the answer is no for static, spherically symmetric RBHs supported by a radial scalar field within a broad class of ST theories. In any RBHs with two-horizon structure, the ratio of the longitudinal scale to the sphere radius must attain an interior maximum. The proper-time derivative of that ratio is associated to the squared propagation speed of odd-parity tensor perturbations by the background field equations in a broad class of scalar-tensor theories. A Lorentzian odd-tensor cone then requires a local minimum instead of a maximum. This conflicts indicate a geometric no-go theorem, covering a broad class of ST theories including spatially covariant gravity, Horndeski theory, quadratic GLPV, DHOST, and U-DHOST theories, and their admissible disformal extensions. Viable RBHs therefore require relaxing at least one geometric or dynamical assumption.
ER -