Hairy Black-holes in Shift-symmetric Theories

Understand

Scalar hair of black holes in theories with a shift symmetry are constrained by the no-hair theorem of Hui and Nicolis, assuming spherical symmetry, time-independence of the scalar field and asymptotic flatness.

• The most studied counterexample is a linear coupling of the scalar with the Gauss-Bonnet invariant.
• However, in this case the norm of the shift-symmetry current $J^2$ diverges at the horizon casting doubts on whether the solution is physically sound.
• We show that this is not an issue since $J^2$ is not a scalar quantity, since $J^\mu$ is not a diff-invariant current in the presence of Gauss-Bonnet.