Kerr black holes with Proca hair

Extending the Proca Lagrangian of a massive complex-valued vector field by self-interaction potential, we construct a large class of spherically symmetric solutions in flat Minkowski background as well as in the self-gravitating case. Our solutions encompass Proca Q-balls and Proca stars known in the literature, but present new features and go beyond the limited region of parameter space charted so far. A special emphasis is set to the domain of existence of the solutions in relation with the coupling constants of the potential and to the critical phenomena limiting this domain.

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“…1 of Ref. [23] and we do not present a similar plot here. We just mention a few qualitative differences : Proca stars (resp.…”

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confidence: 59%

“…Another aspect of these theories that was studied quite extensively is black hole solutions that were found to overcome the no-vector-hair theorems [21,22] exhibiting a vector hair in either the Abelian [23,24] or non-Abelian case [25].…”

Section: Introductionmentioning

confidence: 99%

Proca Q balls and their coupling to gravity

2017

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“…The explicit form of the coefficients can be found in [15,21]. Note that the parameters b (in [21]) and c t (in [15]) relate as b ¼ −c t . In the following we shall dub these as spheroidal prolate (SP) coordinates, cf.…”

Section: The Black-hole Backgroundsmentioning

confidence: 99%

Astrophysical imaging of Kerr black holes with scalar hair

et al. 2016

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We address the astrophysical imaging of a family of deformed Kerr black holes (BHs). These are stationary, asymptotically flat BH spacetimes that are solutions of general relativity minimally coupled to a massive, complex scalar field: Kerr BHs with scalar hair (KBHsSH). Such BHs bifurcate from the vacuum Kerr solution and can be regarded as a horizon within a rotating boson star. In a recent letter [P. V. P. Cunha, C. A. R. Herdeiro, E. Radu, and H. F. Rúnarsson, Phys. Rev. Lett. 115, 211102 (2015).], it was shown that KBHsSH can exhibit very distinct shadows from the ones of their vacuum counterparts. The setup therein, however, considers the light source to be a celestial sphere sufficiently far away from the BH. Here, we analyze KBHsSH surrounded by an emitting torus of matter simulating a more realistic astrophysical environment, and study the corresponding lensing of light as seen by a very faraway observer, to appropriately model ground-based observations of Sgr A Ã . We find that the differences in imaging between KBHsSH and comparable vacuum Kerr BHs remain, albeit less dramatic than those observed for the corresponding shadows in the previous setup. In particular, we highlight two observables that might allow differentiating KBHsSH and Kerr BHs. The first is the angular size of the photon ring (in a Kerr spacetime) or lensing ring (in a KBHSH spacetime), the latter being significantly smaller for sufficiently non-Kerr-like spacetimes. The second is the existence of an edge in the intensity distribution (the photon ring in Kerr spacetime). This edge can disappear for very non-Kerr-like KBHsSH. It is plausible, therefore, that sufficiently precise very long baseline interferometric observations of BH candidates can constrain this model.

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“…We further find that at saturation essentially all the energy and angular momentum extracted from the BH has gone into forming a cloud of complex Proca "hair" with station-ary energy density surrounding the BH. A family of stationary hairy BH solutions with this property and the same matter model was constructed in [28] which is plausibly the same as our end states; it would be interesting to investigate in detail how close these solutions are to what we find at saturation. In our case the Proca clouds persist for the relatively short times we have extended the runs beyond saturation, though this is not adequate to comment on their long-term stability.…”

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confidence: 98%

Superradiant Instability and Backreaction of Massive Vector Fields around Kerr Black Holes

2017

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We study the growth and saturation of the superradiant instability of a complex, massive vector (Proca) field as it extracts energy and angular momentum from a spinning black hole, using numerical solutions of the full Einstein-Proca equations. We concentrate on a rapidly spinning black hole (a = 0.99) and the dominant m = 1 azimuthal mode of the Proca field, with real and imaginary components of the field chosen to yield an axisymmetric stress-tensor, hence spacetime. We find that in excess of 9% of the black hole's mass can be transferred into the field. In all cases studied, the superradiant instability smoothly saturates when the black hole's horizon frequency decreases to match the frequency of the Proca cloud that spontaneously forms around the black hole.Introduction.-A remarkable feature of spinning black holes (BHs) is that a portion of their massup to 29% for extremal spin -can in principle be extracted. One way to realize this liberation of rotational energy is through the interaction of the BH with an impinging wave -be it scalar, electromagnetic, or gravitational -with frequency ω < mΩ BH , where Ω BH is the BH horizon frequency, and m is the azimuthal number of the wave. Waves satisfying this criterion exhibit superradiance, and carry away energy and angular momentum from the BH. An analogous phenomenon can occur for charged BHs, where the electromagnetic energy of the BH is superradiantly transferred to an interacting charged matter field interacting with the BH.Going back to [1] there has been speculation of how superradiance could be combined with a confining mechanism to force the wave to continuously interact with the BH and hence undergo exponential growth -a so called "black hole bomb." The first nonlinear studies of this process were recently undertaken for a charged scalar field around a charged BH in spherical symmetry, both in a reflective cavity in asymptotically flat space [2], and in the naturally confining environment of an asymptotically Anti-de Sitter domain [3].However, there is an exciting possibility that a variation of this scenario could in fact be realized around astrophysical spinning BHs. Massive bosonic fields with Compton wavelength comparable to, or larger than, the horizon radius of a BH can form bound states around the BH, and if the latter is spinning the bound states can grow from a seed perturbation through superradiance [4][5][6]. This implies that stellar mass BHs can probe the existence of ultralight bosons with masses 10 −10 eV that are weakly coupled to ordinary matter and thus difficult to detect by other

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Kerr black holes with Proca hair

Cited by 252 publications

References 138 publications

Proca Q balls and their coupling to gravity

Proca Q balls and their coupling to gravity

Astrophysical imaging of Kerr black holes with scalar hair

Superradiant Instability and Backreaction of Massive Vector Fields around Kerr Black Holes

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