Nonrotating and rotating black holes with secondary disformal hair in a ghost-free metric-affine parity-violating scalar-torsion theory
Abstract
In this paper, we formulate a ghost-free metric-affine scalar-torsion model in which a pseudoscalar field is coupled to the Nieh--Yan density and derivatively coupled to the Einstein-Palatini tensor. The theory is projectively invariant and, in the shift-symmetric sector, depends on the scalar field only through its gradient. After fixing the projective gauge, the independent connection is solved exactly: its symmetric part is the Levi-Civita connection associated with the metric hμν, disformally related to the metric gμν, while its antisymmetric part is a purely axial torsion sourced by vμ=∂μϑ. We identify a degenerate ghost-free branch, α=6β2κ2, for which Ricci-flat geometries in the h-metric frame solve the metric equations and the Noether current vanishes identically. For example, we consider Schwarzschild and Kerr geometries in the h-metric frame, which generate disformal deformations on these geometries from the perspective of the g-metric frame. For the Schwarzschild black hole in the h-metric frame, we construct static and Babichev--Charmousis-like time-dependent scalar profiles, and discuss horizon regularity in Eddington--Finkelstein coordinates. For the Kerr black hole in the h-metric frame, we show that regularity on the rotation axis rules out a nontrivial globally real static fixed-norm scalar profile. For the stationary time-dependent branch, axis regularity and asymptotic reality fix Y0=−q2 and eliminate the angular dependence, yielding a nontrivial future-regular profile in ingoing Kerr coordinates. The Kerr solution with the nontrivial scalar field is stealth only in the h-metric frame. In the g-metric frame, it produces disformal corrections stemming from the nontrivial scalar field profile and it represents secondary disformal scalar hair rather than primary Noether-charge hair.
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BibTeX
@misc{brito2026nonrotating,
title = {{Nonrotating and rotating black holes with secondary disformal hair in a ghost-free metric-affine parity-violating scalar-torsion theory}},
author = {E. Brito and G. Macedo and J. R. Nascimento and A. Yu. Petrov and P. J. Porfírio},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.24041},
eprint = {2606.24041},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.24041},
note = {CC0},
}
RIS
TY - UNPB
TI - Nonrotating and rotating black holes with secondary disformal hair in a ghost-free metric-affine parity-violating scalar-torsion theory
AU - E. Brito
AU - G. Macedo
AU - J. R. Nascimento
AU - A. Yu. Petrov
AU - P. J. Porfírio
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2606.24041
UR - https://arxiv.org/abs/2606.24041
AB - In this paper, we formulate a ghost-free metric-affine scalar-torsion model in which a pseudoscalar field is coupled to the Nieh--Yan density and derivatively coupled to the Einstein-Palatini tensor. The theory is projectively invariant and, in the shift-symmetric sector, depends on the scalar field only through its gradient. After fixing the projective gauge, the independent connection is solved exactly: its symmetric part is the Levi-Civita connection associated with the metric h_μν, disformally related to the metric g_μν, while its antisymmetric part is a purely axial torsion sourced by v_μ=∂_μϑ. We identify a degenerate ghost-free branch, α=6β^2κ^2, for which Ricci-flat geometries in the h-metric frame solve the metric equations and the Noether current vanishes identically. For example, we consider Schwarzschild and Kerr geometries in the h-metric frame, which generate disformal deformations on these geometries from the perspective of the g-metric frame. For the Schwarzschild black hole in the h-metric frame, we construct static and Babichev--Charmousis-like time-dependent scalar profiles, and discuss horizon regularity in Eddington--Finkelstein coordinates. For the Kerr black hole in the h-metric frame, we show that regularity on the rotation axis rules out a nontrivial globally real static fixed-norm scalar profile. For the stationary time-dependent branch, axis regularity and asymptotic reality fix Y_0=−q^2 and eliminate the angular dependence, yielding a nontrivial future-regular profile in ingoing Kerr coordinates. The Kerr solution with the nontrivial scalar field is stealth only in the h-metric frame. In the g-metric frame, it produces disformal corrections stemming from the nontrivial scalar field profile and it represents secondary disformal scalar hair rather than primary Noether-charge hair.
ER -