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Nonrotating and rotating black holes with secondary disformal hair in a ghost-free metric-affine parity-violating scalar-torsion theory

E. Brito1,2,*, G. Macedo2,†, J. R. Nascimento2,‡, A. Yu. Petrov2,§, and P. J. Porfírio2,∥

  • *Contact author: eliasbaj@ufob.edu.br
  • †Contact author: gabriel.santana@academico.ufpb.br
  • ‡Contact author: jroberto@fisica.ufpb.br
  • §Contact author: petrov@fisica.ufpb.br
  • ∥Contact author: pporfirio@fisica.ufpb.br
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Phys. Rev. D 114, 084093 – Published 28 October, 2026

DOI: https://doi.org/10.1103/wdc3-frlv

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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Phys. Rev. D 114, 084093– Published 28 October, 2026
  • Received 13 July 2026
  • Accepted 28 September 2026
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