Abstract
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 and a coupling between the scalar field 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 and the presence of a cosmological constant (which can be either positive or negative), as long as the scalar field remains complex and is regular across the horizon.
- Received 20 April 2020
- Accepted 29 June 2020
DOI:https://doi.org/10.1103/PhysRevD.102.024034
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