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 $h_{\mu \nu }$, disformally related to the metric $g_{\mu \nu }$, while its antisymmetric part is a purely axial torsion sourced by $v_{\mu }={\partial }_{\mu }\vartheta$. We identify a degenerate ghost-free branch, $\alpha =6{\beta }^2{\kappa }^2$, 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.

Close

PrevNext

View figure in article

• Alternative gravity theories
• Classical black holes
• General relativity