Black hole hairs in scalar-tensor gravity and the lack thereof

Understand

Scalar-tensor theories are a natural alternative to general relativity, as they may provide an effective dark energy phenomenology on cosmological scales while passing local tests, but their black hole solutions are still poorly understood.

• Here, we generalize existing no-hair theorems for spherical black holes and specific theories in the scalar-tensor class.
• We show that shift symmetry prevents the appearance of scalar hairs in rotating (asymptotically flat, stationary and axisymmetric) black holes for all theories in the Horndeski/beyond Horndeski/DHOST classes, but for those with a coupling between the scalar and the Gauss--Bonnet invariant.
• Our proof also applies to higher dimensions.