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We show that the spin of dark matter induces a gravitational analog of the electromagnetic Faraday effect, where the polarization of gravitational waves undergoes a rotation as they propagate through a dark matter halo with a non-vanishing axial spin tensor (hypermomentum). An expression for the gravitational rotation angle is provided, which is analogous to the Faraday rotation in optics, and evaluate its significance in astrophysical settings. Although the effect is expected to be small under current observational constraints, we discuss its potential importance in the early universe.

We present a novel asymptotically anti-de Sitter black hole solution with conformally-coupled scalar fields in the first-order formalism of gravity in four dimensions. To do so, we consider a one-parameter extension of conformal transformations by exploiting the fact that the vielbein and spin connection are regarded as independent fields. We solve the field equations analytically and obtain a static black hole solution with nontrivial torsion sourced by the conformal coupling between the scalar field and geometry. The presence of torsion renders the scalar field everywhere regular, while the curvature and torsion singularities coalesce into the origin. We show that this configuration is continuously connected to previously reported solutions in the limit of vanishing torsion and analyze its main properties, focusing on the consequences of the torsional singularity., Comment: References added. Matches published version

This article studies the effects of an arbitrary dark matter spin tensor on the propagation of gravitational wave amplitude in the context of Einstein-Cartan theory. We choose to work with an arbitrary spin tensor because, given our ignorance of the nature of dark matter, it is sensible not to make further hypotheses on its spin and not to assume any particular model for its spin tensor (or its vanishing). The analysis focuses on a \textquotedblleft weak-torsion regime,\textquotedblright\ such that gravitational wave emission, at leading and subleading orders, does not deviate from standard General Relativity. We show that, in principle, the background torsion induced by an eventual dark matter spin component could lead to an anomalous dampening or amplification of the gravitational wave amplitude, after going across a long cosmological distance. We assess the importance of this torsion-induced anomalous amplitude propagation for binary black hole mergers in a way as model-free as possible in Einstein-Cartan gravity. It is possible to prove that at its best, for realistic late-universe cosmological scenarios, the effect is tiny and falls below detection thresholds, even for near-future interferometers such as LISA. Therefore, detecting this effect may not be impossible, but it is still beyond our technological capabilities. As a model-independent result in the Einstein-Cartan context, it also implies that mergers are robust standard sirens without considering any potential dark-matter-induced torsional effects., Comment: 29 pages, 2 figures, accepted for publication in Physics of the Dark Universe