Boson stars and black holes with wavy scalar hair

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In this paper, we follow up on the discovery of a new type of solution in the Einstein-Maxwell system coupled minimally to a self-interacting complex scalar field.

• For sufficiently large gravitational coupling and sufficiently small electromagnetic coupling we demonstrate that boson stars as well as black holes can carry scalar hair that shows a distinct new feature~: a number of spatial oscillations in the scalar field away from the core or horizon, respectively.
• These spatial oscillations appear also in the curvature invariants and hence should be a detectable feature of the space-time.
• As a first hint that this is true, we show that the effective potential for null geodesics in this space-time possesses a local minimum indicating that in the spatial region where oscillations occur a new stable photon sphere should be possible.