Papers by Carlos Herdeiro
Classical and Quantum Gravity, 2016
Bekenstein proved that in Einstein's gravity minimally coupled to one (or many) real, Abelian, Pr... more 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, axisymmetric, 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 [1, 2], that the existence of such clouds at the linear level implies the existence of a new family of BH solutions at the non-linear level. We confirm this expectation and explicitly construct examples of such Kerr black holes 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 [3] 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.
The SO(4) isometry of the extreme Reissner-Nordstrom black hole of N = 1, D = 5 supergravity can ... more The SO(4) isometry of the extreme Reissner-Nordstrom black hole of N = 1, D = 5 supergravity can be partly broken, without breaking any supersymmetry, in two different ways. The "right" solution is a rotating black hole (BMPV); the "left" is interpreted as a black hole in a Gödel universe (GBH). In ten dimensions, both spacetimes are described by deformations of the D1-D5-pp-wave system with the property that the non-trivial Closed Timelike Curves (CTC's) of the five dimensional manifold are absent in the universal covering space of the ten dimensional manifold. In the decoupling limit, the BMPV deformation is normalizable. It corresponds to the vev of an IR relevant operator of dimension ∆ = 1. The Gödel deformation is sub-leading in α ′ unless we take an infinite vorticity limit; in such case it is a non-normalizable perturbation. It corresponds to the insertion of a vector operator of dimension ∆ = 5. Thus we conclude that from the dual (1+1)-CFT viewpoint the SO(4) R-symmetry is broken 'spontaneously' in the BMPV case and explicitly in the Gödel case. * E-mail: [email protected] 1 Different supersymmetric deformations of the D1-D5 system with angular momentum have been considered in ]. fluid and a negative cosmological constant. However, the solution is plagued with Closed Timelike Curves (CTC's), which make the Cauchy problem ill-defined and seemingly violate causality. Still, attempts have been made to make sense of spacetimes with CTC's at the classical level [16] and the discussion concerning their consistency shifted to the quantum realm .
Nuclear Physics B, 2000
Supersymmetric, rotating, asymptotically flat black holes with a regular horizon are rare configu... more Supersymmetric, rotating, asymptotically flat black holes with a regular horizon are rare configurations in string theory. One example is known in five spacetime dimensions, within the toroidal compactification of type IIB string theory. The existence of such special solution is allowed by the existence of a Chern–Simons coupling in the supergravity theory and by the possibility of imposing a self
Classical and Quantum Gravity, 2003
By applying a set of Hassan-Sen transformations and string dualities to the Kerr-Gödel solution o... more By applying a set of Hassan-Sen transformations and string dualities to the Kerr-Gödel solution of minimal D = 5 supergravity we derive a four parameter family of five dimensional solutions in type II string theory. They describe rotating, charged black holes in a rotating background. For zero background rotation, the solution is D = 5 Kerr-Newman; for zero charge it is Kerr-Gödel. In a particular extremal limit the solution describes an asymptotically Gödel BMPV black hole. * by the quantum states . The BMPV spacetime can only be interpreted as a black hole for sufficiently small values of angular momentum; otherwise there is no horizon and the spacetime becomes a non-singular repulson with Closed Timelike Curves passing through any point. On the string theory side unitarity is violated when this happens .
We show how non-near horizon, non-dilatonic p-brane theories can be obtained from two embedding c... more We show how non-near horizon, non-dilatonic p-brane theories can be obtained from two embedding constraints in a flat higher dimensional space with 2 time directions. In particular this includes the construction of D3 branes from a flat 12-dimensional action, and M2 and M5 branes from 13 dimensions. The worldvolume actions are found in terms of fields defined in the embedding space, with the constraints enforced by Lagrange multipliers. * Onderzoeksdirecteur, FWO, Belgium 1 SO(d + 1) for the sphere, SO(d − 1, 2) for AdS
We present a new model of gravity which explicitly breaks Lorentz-invariance by the introduction ... more We present a new model of gravity which explicitly breaks Lorentz-invariance by the introduction of a unit time-like vector field, thereby giving rise to an extra (scalar) degree of freedom. We discuss its cosmology, exact solutions and the dynamics of the scalar mode. We show that it predicts inflation without an inflaton and admits the black hole solutions of General Relativity (GR). We argue that the scalar mode is well behaved and contains none of the pathologies previously found in similar models.
Physical Review D
We have recently reported (arXiv:1403.2757) the existence of Kerr black holes with scalar hair in... more We have recently reported (arXiv:1403.2757) the existence of Kerr black holes with scalar hair in General Relativity minimally coupled to a massive, complex scalar field. These solutions interpolate between boson stars and Kerr black holes. The latter have a well known topologically S^2 ergo-surface (ergo-sphere) whereas the former develop a S^1*S^1 ergo-surface (ergo-torus) in a region of parameter space. We show that hairy black holes always have an ergo-region, and that this region is delimited by either an ergo-sphere or an ergo-Saturn -- i.e. a S^2\oplus (S^1*S^1) ergo-surface. In the phase space of solutions, the ergo-torus can either appear disconnected from the ergo-sphere or pinch off from it. We provide a heuristic argument, based on a measure of the size of the ergo-region, that superradiant instabilities - which are likely to be present - are weaker for hairy black holes than for Kerr black holes with the same global charges. We observe that Saturn-like, and even more re...
Kerr black holes have their angular momentum, $J$, bounded by their mass, $M$: $Jc\leqslant GM^2$... more Kerr black holes have their angular momentum, $J$, bounded by their mass, $M$: $Jc\leqslant GM^2$. There are, however, known black hole solutions violating this Kerr bound. We propose a very simple universal bound on the rotation, rather than on the angular momentum, of four-dimensional, stationary and axisymmetric, asymptotically flat black holes, given in terms of an appropriately defined horizon linear velocity, $v_H$. The $v_H$ bound is simply that $v_H$ cannot exceed the velocity of light. We verify the $v_H$ bound for known black hole solutions, including some that violate the Kerr bound, and conjecture that only extremal Kerr black holes saturate the $v_H$ bound.
Physical Review D, 2015
Under certain conditions sound waves in fluids experience an acoustic horizon with analogue prope... more Under certain conditions sound waves in fluids experience an acoustic horizon with analogue properties to those of a black hole event horizon. In particular, a draining bathtub-like model can give rise to a rotating acoustic horizon and hence a rotating black hole (acoustic) analogue. We show that sound waves, when enclosed in a cylindrical cavity, can form stationary waves around such rotating acoustic black holes. These acoustic perturbations display similar properties to the scalar clouds that have been studied around Kerr and Kerr-Newman black holes; thus they are dubbed acoustic clouds. We make the comparison between scalar clouds around Kerr black holes and acoustic clouds around the draining bathtub explicit by studying also the properties of scalar clouds around Kerr black holes enclosed in a cavity. Acoustic clouds suggest the possibility of testing, experimentally, the existence and properties of black hole clouds, using analog models.
International Journal of Modern Physics D, 2015
We discuss stationary bound states, a.k.a. clouds, for a massless test scalar field around Kerr b... more We discuss stationary bound states, a.k.a. clouds, for a massless test scalar field around Kerr black holes (BHs) and spinning acoustic BH analogues. In view of the absence of a mass term, the trapping is achieved via enclosing the BH -scalar field system in a cavity and imposing Dirichlet or Neumann boundary conditions. We discuss the variation of these bounds states with the discrete parameters that label them, as well as their spatial distribution, complementing results in our previous work [C. L. Benone, L. C. B. Crispino, C. Herdeiro and E. Radu, Phys. Rev. D 91 (2015) 104038].
International Journal of Modern Physics D, 2015
We consider the status of black hole solutions with non-trivial scalar fields but no gauge fields... more We consider the status of black hole solutions with non-trivial scalar fields but no gauge fields, in four dimensional asymptotically flat space-times, reviewing both classical results and recent developments. We start by providing a simple illustration on the physical difference between black holes in electro-vacuum and scalar-vacuum. Next, we review no-scalar-hair theorems. In particular, we detail an influential theorem by Bekenstein and stress three key assumptions: 1) the type of scalar field equation; 2) the spacetime symmetry inheritance by the scalar field; 3) an energy condition. Then, we list regular (on and outside the horizon), asymptotically flat BH solutions with scalar hair, organizing them by the assumption which is violated in each case and distinguishing primary from secondary hair. We provide a table summary of the state of the art. a This statement applies to single-BH solutions. Multi-BH solutions, described by the Majumdar-Papapetrou metric, also exist in electro-vacuum. Moreover, if one is willing to consider magnetic charges, by electromagnetic duality there are also magnetically charged and dyonic BHs. None of these, however, seem likely to arise as the endpoint of gravitational collapse. May 4, 2015 2:37 WSPC/INSTRUCTION FILE reviewscalarhair Asymptotically flat black holes with scalar hair: a review 3
The Twelfth Marcel Grossmann Meeting - On Recent Developments in Theoretical and Experimental General Relativity Astrophysics and Relativistic Field Theories - Proceedings of the MG12 Meeting on General Relativity, 2012
We present a gravito-electromagnetic analogy stemming from the tidal dynamics of both theories, a... more We present a gravito-electromagnetic analogy stemming from the tidal dynamics of both theories, and based on exact and covariant equations: the gravitational and electromagnetic worldline deviations, the electromagnetic force exerted on a magnetic dipole and the analogous gravitational force on a spinning pole-dipole test particle. This analogy is made explicit in the tidal tensor formalism, within which both Maxwell's and the temporal part of Einstein's equations are exactly cast as equations for tidal tensors and sources, allowing for a direct and transparent comparison between the two interactions.
Kerr black holes with scalar hair are solutions of the Einstein-Klein-Gordon field equations desc... more Kerr black holes with scalar hair are solutions of the Einstein-Klein-Gordon field equations describing regular (on and outside an event horizon), asymptotically flat black holes with scalar hair [1]. These black holes interpolate continuously between the Kerr solution and rotating boson stars in D = 4 spacetime dimensions. Here we provide details on their construction, discussing properties of the ansatz, the field equations, the boundary conditions and the numerical strategy. Then, we present an overview of the parameter space of the solutions, and describe in detail the space-time structure of the black holes exterior geometry and of the scalar field for a sample of reference solutions. Phenomenological properties of potential astrophysical interest are also discussed, and the stability properties and possible generalizations are commented on. As supplementary material to this paper we make available numerical data files for the sample of reference solutions discussed, for public use. * [email protected] † [email protected]
Physical Review D, 2008
We propose a new approach to a physical analogy between General Relativity and Electromagnetism, ... more We propose a new approach to a physical analogy between General Relativity and Electromagnetism, based on tidal tensors of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations. The following realisations of the analogy are given. The first one matches linearised gravitational tidal tensors to exact electromagnetic tidal tensors in Minkwoski
International Journal of Modern Physics D, 2014
We show that scalar hair can be added to rotating, vacuum black holes (BHs) of general relativity... more We show that scalar hair can be added to rotating, vacuum black holes (BHs) of general relativity. These hairy black holes (HBHs) clarify a lingering question concerning gravitational solitons: Whether a BH can be added at the centre of a boson star (BS), as it typically can for other solitons. We argue that it can, but only if it is spinning. The existence of such HBHs is related to the Kerr superradiant instability triggered by a massive scalar field. This connection leads to the following conjecture: a (hairless) BH, which is afflicted by the superradiant instability of a given field, must allow hairy generalizations with that field.
We consider Neveu-Schwarz pp-waves with spacetime supersymmetry. Upon compactification of a space... more We consider Neveu-Schwarz pp-waves with spacetime supersymmetry. Upon compactification of a spacelike direction, these backgrounds develop Closed Null Curves (CNCs) and Closed Timelike Curves (CTCs), and are U-dual to supersymmetric Gödel type universes. We study classical and quantum strings in this background, with emphasis on the strings winding around the compact direction. We consider two types of strings: long strings stabilized by NS flux and rotating strings which are stabilized against collapse by angular momentum. Some of the latter strings wrap around CNCs and CTCs, and are thus a potential source of pathology. We analyze the partition function, and in particular discuss the effects of these string states. Although our results are not conclusive, the partition function seems to be dramatically altered due to the presence of CNCs and CTCs. We discuss some interpretations of our results, including a possible sign of unitary violation.
We discuss the relation between solutions admitting Killing spinors of minimal supergravities in ... more We discuss the relation between solutions admitting Killing spinors of minimal supergravities in five dimensions and four dimensional complex geometries. In the ungauged case (vanishing cosmological constant Λ = 0) the solutions are determined in terms of a hyper-Kähler base space; in the gauged case (Λ < 0) the complex geometry is Kähler; in the de Sitter case (Λ > 0) the complex geometry is hyper-Kähler with torsion (HKT). In the latter case some details of the derivation are given. The method for constructing explicit solutions is discussed in each case.
An explicit global and unique isometric embedding into hyperbolic 3-space, H 3 , of an axisymmetr... more An explicit global and unique isometric embedding into hyperbolic 3-space, H 3 , of an axisymmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H 3 of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U (1) isometry. As an example, we exhibit the global embedding of the Kerr-Newman event horizon into H 3 , for arbitrary values of the angular momentum. For this example, considering a quotient of H 3 by the Picard group, we show that the hyperbolic embedding fits in a fundamental domain of the group up to a slightly larger value of the angular momentum than the limit for which a global embedding into Euclidean 3-space is possible. An embedding of the double-Kerr event horizon is also presented, as an example of an embedding which cannot be made global.
Proceedings of the International Astronomical Union, 2009
The similarities between linearized gravity and electromagnetism are known since the early days o... more The similarities between linearized gravity and electromagnetism are known since the early days of General Relativity. Using an exact approach based on tidal tensors, we show that such analogy holds only on very special conditions and depends crucially on the reference frame. This places restrictions on the validity of the "gravito-electromagnetic" equations commonly found in the literature.
Uploads
Papers by Carlos Herdeiro