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In this work we study static black holes in the regularized 4DEinstein-Gauss-Bonnet theory of gravity; a shift-symmetric scalar-tensor theorythat belongs to the Horndeski class. This theory features a simple black holesolution that can be written in closed form, and which we show is the uniquestatic, spherically-symmetric and asymptotically-flat black hole vacuumsolution of the theory. We further show that no asymptotically-flat,time-dependent, spherically-symmetric perturbations to this geometry areallowed, which suggests that it may be the only spherically-symmetric vacuumsolution that this theory admits (a result analogous to Birkhoff's theorem).Finally, we consider the thermodynamic properties of these black holes, andfind that their final state after evaporation is a remnant with a sizedetermined by the coupling constant of the theory. We speculate that remnantsof this kind from primordial black holes could act as dark matter, and weconstrain the parameter space for their formation mass, as well as the couplingconstant of the theory.

Black Holes in the Scalar-Tensor Formulation of 4D Einstein-Gauss-Bonnet Gravity: Uniqueness of Solutions, and a New Candidate for Dark Matter