Kerr black holes with Proca hair

By Carlos A. R. Herdeiro, Eugen Radu, H. R'unarsson. 2016

257 citations recorded by the source corpus.

Bekenstein proved that in Einstein's gravity minimally coupled to one (or many) real, Abelian, Proca field, stationary black holes (BHs) cannot have Proca hair. Dropping Bekenstein's assumption that matter inherits spacetime symmetries, we show this model admits asymptotically flat, stationary, axi-symmetric, regular on and outside an event horizon BHs with Proca hair, for an even number of real (or an arbitrary number of complex) Proca fields. To establish it, we start by showing that a test, complex Proca field can form bound states, with real frequency, around Kerr BHs: stationary Proca clouds. These states exist at the threshold of superradiance. It was conjectured in [, ], that the existence of such clouds at the linear level implies the existence of a new family of BH solutions at the nonlinear level. We confirm this expectation and explicitly construct examples of such Kerr BHs with Proca hair (KBHsPH). For a single complex Proca field, these BHs form a countable number of families with three continuous parameters (ADM mass, ADM angular momentum and Noether charge). They branch off from the Kerr solutions that can support stationary Proca clouds and reduce to Proca stars [] when the horizon size vanishes. We present the domain of existence of one family of KBHsPH, as well as its phase space in terms of ADM quantities. Some physical properties of the solutions are discussed; in particular, and in contrast with Kerr BHs with scalar hair, some spacetime regions can be counter-rotating with respect to the horizon. We further establish a no-Proca-hair theorem for static, spherically symmetric BHs but allowing the complex Proca field to have a harmonic time dependence, which shows BHs with Proca hair in this model require rotation and have no static limit. KBHsPH are also disconnected from Kerr–Newman BHs with a real, massless vector field.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/9af1098c8ded3d4aeceaa70c3258e81f0a18642e

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Citations in the corpus

Dynamical boson stars (2012, background): “8 for a description of Proca stars) were constructed in [253].”
Shadows and strong gravitational lensing: a brief review (2018, methodology): “Among these models, Kerr BHs with bosonic hair have gathered attention recently, being both physically reasonable and minimally coupled to 4D gravity [32,47,48,54].”
Shadow casted by a Konoplya-Zhidenko rotating non-Kerr black hole (2017, background): “Moreover, for a Kerr black hole with Proca hair [31], the black hole shadow has a cusp silhouette as the black hole parameters lie in a certain range [32].”
Superradiance (2015, background): “Solutions with complex Proca hair were also constructed and shown to share very similar properties to the solutions presented above [509, 111].”
Black holes with scalar hair in light of the Event Horizon Telescope (2020, background): “For an inevitably incomplete list of important studies related to the construction and identification of observational signatures of HBHs in various theories of gravity or in the presence of various different types of matter fields, see for instance [5–54].”