No static regular black holes in Einstein-complex-scalar-Gauss-Bonnet gravity

In this brief report, we investigate the existence of four-dimensional static spherically symmetric black holes (BHs) in the Einstein-complex-scalar-Gauss-Bonnet gravity with an arbitrary potential V(ϕ) and a coupling f(ϕ) between the scalar field ϕ and the Gauss-Bonnet (GB) term. We find that static regular BH solutions with complex scalar hairs do not exist. This conclusion does not depend on the coupling between the GB term and the scalar field nor on the scalar potential V(ϕ) and the presence of a cosmological constant Λ (which can be either positive or negative), as long as the scalar field remains complex and is regular across the horizon.

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revtex4, no figures and tables. Version to appear in Phys. Rev. D

General relativity, alternative theories of gravity
field theory: scalar
potential: scalar
hair: scalar
symmetry: rotation
gravitation: model
black hole
cosmological constant
horizon
Gauss-Bonnet term

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