152 research outputs found

    Wiggly tails: a gravitational wave signature of massive fields around black holes

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    Massive fields can exist in long-lived configurations around black holes. We examine how the gravitational wave signal of a perturbed black hole is affected by such `dirtiness' within linear theory. As a concrete example, we consider the gravitational radiation emitted by the infall of a massive scalar field into a Schwarzschild black hole. Whereas part of the scalar field is absorbed/scattered by the black hole and triggers gravitational wave emission, another part lingers in long-lived quasi-bound states. Solving numerically the Teukolsky master equation for gravitational perturbations coupled to the massive Klein-Gordon equation, we find a characteristic gravitational wave signal, composed by a quasi-normal ringing followed by a late time tail. In contrast to `clean' black holes, however, the late time tail contains small amplitude wiggles with the frequency of the dominating quasi-bound state. Additionally, an observer dependent beating pattern may also be seen. These features were already observed in fully non-linear studies; our analysis shows they are present at linear level, and, since it reduces to a 1+1 dimensional numerical problem, allows for cleaner numerical data. Moreover, we discuss the power law of the tail and that it only becomes universal sufficiently far away from the `dirty' black hole. The wiggly tails, by constrast, are a generic feature that may be used as a smoking gun for the presence of massive fields around black holes, either as a linear cloud or as fully non-linear hair.Comment: 6 pages, 4 figure

    On the interaction between two Kerr black holes

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    The double-Kerr solution is generated using both a Backlund transformation and the Belinskii-Zakharov inverse-scattering technique. We build a dictionary between the parametrisations naturally obtained in the two methods and show their equivalence. We then focus on the asymptotically flat double-Kerr system obeying the axis condition which is Z_2^\phi invariant; for this system there is an exact formula for the force between the two black holes, in terms of their physical quantities and the coordinate distance. We then show that 1) the angular velocity of the two black holes decreases from the usual Kerr value at infinite distance to zero in the touching limit; 2) the extremal limit of the two black holes is given by |J|=cM^2, where c depends on the distance and varies from one to infinity as the distance decreases; 3) for sufficiently large angular momentum the temperature of the black holes attains a maximum at a certain finite coordinate distance. All of these results are interpreted in terms of the dragging effects of the system.Comment: 19 pages, 4 figures. v2: changed statement about thermodynamical equilibrium in section 3; minor changes; added references. v3: added references to previous relevant work; removed one equation (see note added); other minor corrections; final version to be published in JHE

    Spherical electro-vacuum black holes with resonant, scalar QQ-hair

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    The asymptotically flat, spherical, electro-vacuum black holes (BHs) are shown to support static, spherical configurations of a gauged, self-interacting, scalar field, minimally coupled to the geometry. Considering a QQ-ball type potential for the scalar field, we dub these configurations QQ-clouds, in the test field approximation. The clouds exist under a resonance condition, at the threshold of (charged) superradiance. This is similar to the stationary clouds supported by Kerr BHs, which exist for a synchronisation condition, at the threshold of (rotational) superradiance. In contrast with the rotating case, however, QQ-clouds require the scalar field to be massive and self-interacting; no similar clouds exist for massive but free scalar fields. First, considering a decoupling limit, we construct QQ-clouds around Schwarzschild and Reissner-Nordstr\"om BHs, showing there is always a mass gap. Then, we make the QQ-clouds backreact, and construct fully non-linear solutions of the Einstein-Maxwell-gauged scalar system describing spherical, charged BHs with resonant, scalar QQ-hair. Amongst other properties, we observe there is non-uniqueness of charged BHs in this model and the QQ-hairy BHs can be entropically preferred over Reissner-Nordstr\"om, for the same charge to mass ratio; some QQ-hairy BH solutions can be overcharged. We also discuss how some well known no-hair theorems in the literature, applying to electro-vacuum plus minimally coupled scalar fields, are circumvented by this new type of BHs.Comment: 18 pages, 5 figures; v2. typos corrected, matches published versio

    Stationary scalar and vector clouds around Kerr-Newman black holes

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    Massive bosons in the vicinity of Kerr-Newman black holes can form pure bound states when their phase angular velocity fulills the synchronisation condition, i.e. at the threshold of superradiance. The presence of these stationary clouds at the linear level is intimately linked to the existence of Kerr black holes with synchronised hair at the non-linear level. These configurations are very similar to the atomic orbitals of the electron in a hydrogen atom. They can be labeled by four quantum numbers: nn, the number of nodes in the radial direction; â„“\ell, the orbital angular momentum; jj, the total angular momentum; and mjm_j, the azimuthal total angular momentum. These synchronised configurations are solely allowed for particular values of the black hole's mass, angular momentum and electric charge. Such quantization results in an existence surface in the three-dimensional parameter space of Kerr-Newman black holes. The phenomenology of stationary scalar clouds has been widely addressed over the last years. However, there is a gap in the literature concerning their vector cousins. Following the separability of the Proca equation in Kerr(-Newman) spacetime, this work explores and compares scalar and vector stationary clouds around Kerr and Kerr-Newman black holes, extending previous research.Comment: 17 pages, 6 figures. Contribution to Selected Papers of the Fifth Amazonian Symposium on Physics (accepted in IJMPD

    Shadows and strong gravitational lensing: a brief review

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    For ultra compact objects (UCOs), Light Rings (LRs) and Fundamental Photon Orbits (FPOs) play a pivotal role in the theoretical analysis of strong gravitational lensing effects, and of BH shadows in particular. In this short review, specific models are considered to illustrate how FPOs can be useful in order to understand some non-trivial gravitational lensing effects. This paper aims at briefly overviewing the theoretical foundations of these effects, touching also some of the related phenomenology, both in General Relativity (GR) and alternative theories of gravity, hopefully providing some intuition and new insights for the underlying physics, which might be critical when testing the Kerr black hole hypothesis.Comment: 32 pages, 9 figures; Review paper in the General Relativity and Gravitation (GRG) Topical Collection "Testing the Kerr spacetime with gravitational-wave and electromagnetic observations" (Guest Editor: Emanuele Berti); v2: Typo corrected and two references adde
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