arXiv subjects

Carlos A. R. Herdeiro

Publications and source records attributed to Carlos A. R. Herdeiro.

At least 127 records · Page 7Linked to original sources

arXiv2016

Kerr-Newman black holes with scalar hair

We construct electrically charged Kerr black holes (BHs) with scalar hair. Firstly, we take an uncharged scalar field, interacting with the electromagnetic field only indirectly, via the background metric. The corresponding family of solutions, dubbed Kerr-Newman BHs with ungauged scalar hair, reduces to (a sub-family of) Kerr-Newman BHs in the limit of vanishing scalar hair and to uncharged rotating boson stars in the limit of vanishing horizon. It adds one extra parameter to the uncharged solutions: the total electric charge. This leading electromagnetic multipole moment is unaffected by the scalar hair and can be computed by using Gauss's law on any closed 2-surface surrounding (a spatial section of) the event horizon. By contrast, the first sub-leading electromagnetic multipole -- the magnetic dipole moment --, gets suppressed by the scalar hair, such that the gyromagnetic ratio is always smaller than the Kerr-Newman value ($g=2$). Secondly, we consider a gauged scalar field and obtain a family of Kerr-Newman BHs with gauged scalar hair. The electrically charged scalar field now stores a part of the total electric charge, which can only be computed by applying Gauss' law at spatial infinity and introduces a new solitonic limit -- electrically charged rotating boson stars. In both cases, we analyse some physical properties of the solutions.

gr-qc↗

arXiv2016

Iron K$α$ line of Kerr black holes with scalar hair

Recently, a family of hairy black holes in 4-dimensional Einstein gravity minimally coupled to a complex, massive scalar field was discovered~\cite{hbh}. Besides the mass $M$ and spin angular momentum $J$, these objects are characterized by a Noether charge $Q$, measuring the amount of scalar hair, which is not associated to a Gauss law and cannot be measured at spatial infinity. Introducing a dimensionless scalar hair parameter $q$, ranging from 0 to 1, we recover (a subset of) Kerr black holes for $q=0$ and a family of rotating boson stars for $q=1$. In the present paper, we explore the possibility of measuring $q$ for astrophysical black holes with current and future X-ray missions. We study the iron K$α$ line expected in the reflection spectrum of such hairy black holes and we simulate observations with Suzaku and eXTP. As a proof of concept, we point out, by analyzing a sample of hairy black holes, that current observations can already constrain the scalar hair parameter $q$, because black holes with $q$ close to 1 would have iron lines definitively different from those we observe in the available data. We conclude that a detailed scanning of the full space of solutions, together with data from the future X-ray missions, like eXTP, will be able to put relevant constraints on the astrophysical realization of Kerr black holes with scalar hair.

gr-qc↗

arXiv2016

Violations of the Kerr and Reissner-Nordstrom bounds: horizon versus asymptotic quantities

A central feature of the most elementary rotating black hole (BH) solution in General Relativity is the Kerr bound, which, for vacuum Kerr BHs, can be expressed either in terms of the ADM or the horizon "charges". This bound, however, is not a fundamental properties of General Relativity and stationary, asymptotically flat, regular (on and outside an event horizon) BHs are known to violate the Kerr bound, both in terms of their ADM and horizon quantities. Examples include the recently discovered Kerr BHs with scalar or Proca hair. Here, we point the fact that the Kerr bound in terms of horizon quantities is also violated by well-known rotating and charged solutions, known in closed form, such as the Kerr-Newman and Kerr-Sen BHs. For the former, moreover, we observe that the Reissner-Nordstrom (RN) bound is also violated in terms of horizon quantities, even in the static (i.e RN) limit. For the latter, by contrast, the existence of charged matter outside the horizon, allows a curious invariance of the charge to mass ratio, between ADM and horizon quantities. Regardless of the Kerr bound violation, we show that in all case, the event horizon linear velocity never exceeds the speed of light. Finally, we suggest a new type of informative parameterization for BH spacetimes where part of the asymptotic charges is supported outside the horizon.

gr-qc↗

arXiv2016

Shadows of Kerr black holes with and without scalar hair

For an observer, the Black Hole (BH) shadow is the BH's apparent image in the sky due to the gravitational lensing of nearby radiation, emitted by an external source. A recent class of solutions dubbed Kerr BHs with scalar hair possess smaller shadows than the corresponding Kerr BHs and, under some conditions, novel exotic shadow shapes can arise. Thus, these hairy BHs could potentially provide new shadow templates for future experiments such as the Event Horizon Telescope. In order to obtain the shadows, the backward ray-tracing algorithm is briefly introduced, followed by numerical examples of shadows of Kerr BHs with scalar hair contrasting with the Kerr analogues. Additionally, an analytical solution for the Kerr shadow is derived in closed form for a ZAMO observer at an arbitrary position.

gr-qc↗

arXiv2016

Spinning boson stars and Kerr black holes with scalar hair: the effect of self-interactions

Self-interacting boson stars have been shown to alleviate the astrophysically low maximal mass of their non-self-interacting counterparts. We report some physical features of spinning self-interacting boson stars, namely their compactness, the occurence of ergo-regions and the scalar field profiles, for a sample of values of the coupling parameter. The results agree with the general picture that these boson stars are comparatively less compact than the non-self-interacting ones. We also briefly discuss the effect of scalar self-interactions on the properties of Kerr black holes with scalar hair.

gr-qc↗

arXiv2015

Shadows of Kerr black holes with scalar hair

Using backwards ray tracing, we study the shadows of Kerr black holes with scalar hair (KBHsSH). KBHsSH interpolate continuously between Kerr BHs and boson stars (BSs), so we start by investigating the lensing of light due to BSs. Moving from the weak to the strong gravity region, BSs - which by themselves have no shadows - are classified, according to the lensing produced, as: $(i)$ non-compact, which yield no multiple images; $(ii)$ compact, which produce an increasing number of Einstein rings and multiple images of the whole celestial sphere; $(iii)$ ultra-compact, which possess light rings, yielding an infinite number of images with (we conjecture) a self-similar structure. The shadows of KBHsSH, for Kerr-like horizons and non-compact BS-like hair, are analogous to, but distinguishable from, those of comparable Kerr BHs. But for non-Kerr-like horizons and ultra-compact BS-like hair, the shadows of KBHsSH are drastically different: novel shapes arise, sizes are considerably smaller and multiple shadows of a single BH become possible. Thus, KBHsSH provide quantitatively and qualitatively new templates for ongoing (and future) very large baseline interferometry (VLBI) observations of BH shadows, such as those of the Event Horizon Telescope.

gr-qc↗

arXiv2015

Kerr black holes with self-interacting scalar hair: hairier but not heavier

The maximal ADM mass for (mini-)boson stars (BSs) -- gravitating solitons of Einstein's gravity minimally coupled to a free, complex, mass $μ$, Klein-Gordon field -- is $M_{\rm ADM}^{\rm max}\sim M_{Pl}^2/μ$. Adding quartic self-interactions to the scalar field theory, described by the Lagrangian $\mathcal{L}_I=λ|Ψ|^4$, the maximal ADM mass becomes $M_{\rm ADM}^{\rm max}\sim \sqrtλM_{Pl}^3/μ^2$. Thus, for mini-BSs, astrophysically interesting masses require ultra-light scalar fields, whereas self-interacting BSs can reach such values for bosonic particles with Standard Model range masses. We investigate how these same self-interactions affect Kerr black holes with scalar hair (KBHsSH) [1], which can be regarded as (spinning) BSs in stationary equilibrium with a central horizon. Remarkably, whereas the ADM mass scales in the same way as for BSs, the \textit{horizon mass} $M_H$ does not increases with the coupling $λ$, and, for fixed $μ$, it is maximized at the "Hod point", corresponding to the extremal Kerr black hole obtained in the vanishing hair limit. This mass is always $M_{\rm H}^{\rm max }\sim M_{\rm Pl}^2/μ$. Thus, introducing these self-interactions, the black hole spacetimes may become considerably "hairier" but the trapped regions cannot become "heavier". We present evidence this observation also holds in a model with $\mathcal{L}_I= β|Ψ|^6-λ|Ψ|^4$; if it extends to \textit{general} scalar field models, KBHsSH with astrophysically interesting horizon masses \textit{require} ultra-light scalar fields. Their existence, therefore, would be a smoking gun for such (beyond the Standard Model) particles.

gr-qc↗

arXiv2015

Proca Stars: gravitating Bose-Einstein condensates of massive spin 1 particles

We establish that massive complex Abelian vector fields (mass $μ$) can form gravitating solitons, when minimally coupled to Einstein's gravity. Such Proca stars (PSs) have a stationary, everywhere regular and asymptotically flat geometry. The Proca field, however, possesses a harmonic time dependence (frequency $w$), realizing Wheeler's concept of geons for an Abelian spin 1 field. We obtain PSs with both a spherically symmetric (static) and an axially symmetric (stationary) line element. The latter form a countable number of families labelled by an integer $m\in \mathbb{Z}^+$. PSs, like (scalar) boson stars, carry a conserved Noether charge, and are akin to the latter in many ways. In particular, both types of stars exist for a limited range of frequencies and there is a maximal ADM mass, $M_{max}$, attained for an intermediate frequency. For spherically symmetric PSs (rotating PSs with $m=1,2,3$), $M_{max}\simeq 1.058 M_{Pl}^2/μ$ ($M_{max}\simeq 1.568,\, 2.337, \, 3.247 \, M_{Pl}^2/μ$), slightly larger values than those for (mini-)boson stars. We establish perturbative stability for a subset of solutions in the spherical case and anticipate a similar conclusion for fundamental modes in the rotating case. The discovery of PSs opens many avenues of research, reconsidering five decades of work on (scalar) boson stars, in particular as possible dark matter candidates.

gr-qc↗

arXiv2015

How fast can a black hole rotate?

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.

gr-qc↗

arXiv2014

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

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.

gr-qc↗

arXiv2014

Kerr black holes with scalar hair

We present a family of solutions of Einstein's gravity minimally coupled to a complex, massive scalar field, describing asymptotically flat, spinning black holes with scalar hair and a regular horizon. These hairy black holes (HBHs) are supported by rotation and have no static limit. Besides mass M and angular momentum J, they carry a conserved, continuous Noether charge Q measuring the scalar hair. HBHs branch off from the Kerr metric at the threshold of the superradiant instability and reduce to spinning boson stars in the limit of vanishing horizon area. They overlap with Kerr black holes for a set of (M,J) values. A single Killing vector field preserves the solutions, tangent to the null geodesic generators of the event horizon. HBHs can exhibit sharp physical differences when compared to the Kerr solution, such as J/M^2>1, quadrupole moment larger than J^2/M and larger orbital angular velocity at the innermost stable circular orbit. Families of HBHs connected to the Kerr geometry should exist in scalar (and other) models with more general self interactions.

gr-qc↗

arXiv2014

A new spin on black hole hair

We show that scalar hair can be added to rotating, vacuum black holes of general relativity. These hairy black holes (HBHs) clarify a lingering question concerning gravitational solitons: if a black hole can be added at the centre of a boson star, 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) black hole which is afflicted by the superradiant instability of a given field must allow hairy generalizations with that field.

gr-qc↗

arXiv2013

Time evolution of superradiant instabilities for charged black holes in a cavity

Frequency domain studies have recently demonstrated that charged scalar fields exhibit fast growing superradiant instabilities when interacting with charged black holes in a cavity. Here, we present a time domain analysis of the long time evolution of test charged scalar field configurations on the Reissner-Nordström background, with or without a mirror-like boundary condition. Initial data is taken to be either a Gaussian wave packet or a regularised (near the horizon) quasi-bound state. Then, Fourier transforming the data obtained in the evolution confirms the results obtained in the frequency domain analysis, in particular for the fast growing modes. We show that spherically symmetric (l=0) modes have even faster growth rates than the l=1 modes for `small' field charge. Thus, our study confirms that this setup is particularly promising for considering the non-linear development of the superradiant instability, since the fast growth makes the signal overcome the numerical error that dominates for small growth rates, and the analysis may be completely done in spherical symmetry.

gr-qc↗

arXiv2013

Rapid growth of superradiant instabilities for charged black holes in a cavity

Confined scalar fields, either by a mass term or by a mirror-like boundary condition, have unstable modes in the background of a Kerr black hole. Assuming a time dependence as $e^{-iωt}$, the growth time-scale of these unstable modes is set by the inverse of the (positive) imaginary part of the frequency, Im$(ω)$, which reaches a maximum value of the order of Im$(ω)M\sim 10^{-5}$, attained for a mirror-like boundary condition, where $M$ is the black hole mass. In this paper we study the minimally coupled Klein-Gordon equation for a charged scalar field in the background of a Reissner-Nordström black hole and show that the unstable modes, due to a mirror-like boundary condition, can grow several orders of magnitude faster than in the rotating case: we have obtained modes with up to Im$(ω)M\sim 0.07$. We provide an understanding, based on an analytic approximation, to why the instability in the charged case has a smaller timescale than in the rotating case. This faster growth, together with the spherical symmetry, makes the charged case a promising model for studies of the fully non-linear development of superradiant instabilities.

gr-qc↗

arXiv2013

Stationary scalar configurations around extremal charged black holes

We consider the minimally coupled Klein-Gordon equation for a charged, massive scalar field in the non-extremal Reissner-Nordström background. Performing a frequency domain analysis, using a continued fraction method, we compute the frequencies ωfor quasi-bound states. We observe that, as the extremal limit for both the background and the field is approached, the real part of the quasi-bound states frequencies $\mathcal{R}(ω)$ tends to the mass of the field and the imaginary part $\mathcal{I}(ω)$ tends to zero, for any angular momentum quantum number $\ell$. The limiting frequencies in this double extremal limit are shown to correspond to a distribution of extremal scalar particles, at stationary positions, in no-force equilibrium configurations with the background. Thus, generically, these stationary scalar configurations are regular at the event horizon. If, on the other hand, the distribution contains scalar particles at the horizon, the configuration becomes irregular therein, in agreement with no hair theorems for the corresponding Einstein-Maxwell-scalar field system.

gr-qc↗

arXiv2011

Mathisson's helical motions for a spinning particle --- are they unphysical?

It has been asserted in the literature that Mathisson's helical motions are unphysical, with the argument that their radius can be arbitrarily large. We revisit Mathisson's helical motions of a free spinning particle, and observe that such statement is unfounded. Their radius is finite and confined to the disk of centroids. We argue that the helical motions are perfectly valid and physically equivalent descriptions of the motion of a spinning body, the difference between them being the choice of the representative point of the particle, thus a gauge choice. We discuss the kinematical explanation of these motions, and we dynamically interpret them through the concept of hidden momentum. We also show that, contrary to previous claims, the frequency of the helical motions coincides, even in the relativistic limit, with the zitterbewegung frequency of the Dirac equation for the electron.

gr-qc↗

arXiv2010

The Casimir spectrum revisited

We examine the mathematical and physical significance of the spectral density sigma(w) introduced by Ford in Phys. Rev. D38, 528 (1988), defining the contribution of each frequency to the renormalised energy density of a quantum field. Firstly, by considering a simple example, we argue that sigma(w) is well defined, in the sense of being regulator independent, despite an apparently regulator dependent definition. We then suggest that sigma(w) is a spectral distribution, rather than a function, which only produces physically meaningful results when integrated over a sufficiently large range of frequencies and with a high energy smooth enough regulator. Moreover, sigma(w) is seen to be simply the difference between the bare spectral density and the spectral density of the reference background. This interpretation yields a simple `rule of thumb' to writing down a (formal) expression for sigma(w) as shown in an explicit example. Finally, by considering an example in which the sign of the Casimir force varies, we show that the spectrum carries no manifest information about this sign; it can only be inferred by integrating sigma(w).

quant-ph↗

arXiv2009

Reference Frames and the Physical Gravito-Electromagnetic Analogy

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.

gr-qc↗