arXiv subjects

Carlos A. R. Herdeiro

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

At least 73 records · Page 4Linked to original sources

arXiv2020

Asymptotically flat, spherical, self-interacting scalar, Dirac and Proca stars

We present a comparative analysis of the self-gravitating solitons arising in the Einstein-Klein-Gordon, Einstein-Dirac and Einstein-Proca models, for the particular case of static, spherically symmetric spacetimes. Differently from the previous study arXiv:1708.05674, the matter fields possess suitable self-interacting terms in the Lagrangians, which allow for the existence of $Q$-ball--type solutions for these models in the flat spacetime limit. In spite of this important difference, our analysis shows that the high degree of universality observed in arXiv:1708.05674 remains, and various spin-independent common patterns are observed.

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arXiv2020

Kerr black holes with synchronised axionic hair

We construct and analyse Kerr black holes (BHs) with synchronised axionic hair. These are the BH generalisations of the recently constructed rotating axion boson stars arXiv:2005.05982. Such BHs are stationary, axially symmetric, asymptotically flat solutions of the complex Einstein-Klein-Gordon theory with a QCD axion-like potential. They are regular everywhere on and outside the event horizon. The potential is characterised by two parameters: the mass of the axion-like particle, $m_a$ and the decay constant $f_a$. The limit $f_a \rightarrow \infty$ recovers the original example of Kerr BHs with synchronised scalar hair arXiv:1403.2757. The effects of the non-linearities in the potential become important for $f_a \lesssim 1$. We present an overview of the parameter space of the solutions together with a study of their basic geometric and phenomenological properties, for an illustrative value of the coupling that yields a non-negligible impact of the self-interactions.

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arXiv2020

Shadows of charged rotating black holes: Kerr-Newman versus Kerr-Sen

Celebrating the centennial of its first experimental test, the theory of General Relativity (GR) has successfully and consistently passed all subsequent tests with flying colours. It is expected, however, that at certain scales new physics, in particular in the form of quantum corrections, will emerge, changing some of the predictions of GR, which is a classical theory. In this respect, black holes (BHs) are natural configurations to explore the quantum effects on strong gravitational fields. BH solutions in the low-energy effective field theory description of the heterotic string theory, which is one of the leading candidates to describe quantum gravity, have been the focus of many studies in the last three decades. The recent interest in strong gravitational lensing by BHs, in the wake of the Event Horizon Telescope observations, suggests comparing the BH lensing in both GR and heterotic string theory, in order to assess the phenomenological differences between these models. In this work, we investigate the differences in the shadows of two charged BH solutions with rotation: one arising in the context of GR, namely the Kerr-Newman solution, and the other within the context of low-energy heterotic string theory, the Kerr-Sen solution. We show and interpret, in particular, that the stringy BH always has a larger shadow, for the same physical parameters and observation conditions.

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arXiv2020

Spinning black holes with a separable Hamilton-Jacobi equation from a modified Newman-Janis algorithm

Obtaining solutions of the Einstein field equations describing spinning compact bodies is typically challenging. The Newman-Janis algorithm provides a procedure to obtain rotating spacetimes from a static, spherically symmetric, seed metric. It is not guaranteed, however, that the resulting rotating spacetime solves the same field equations as the seed. Moreover, the former may not be circular, and thus expressible in Boyer-Lindquist-like coordinates. Amongst the variations of the original procedure, a modified Newman-Janis algorithm (MNJA) has been proposed that, by construction, originates a circular, spinning spacetime, expressible in Boyer-Lindquist-like coordinates. As a down side, the procedure introduces an ambiguity, that requires extra assumptions on the matter content of the model. In this paper we observe that the rotating spacetimes obtained through the MNJA always admit separability of the Hamilton-Jacobi equation for the case of null geodesics, in which case, moreover, the aforementioned ambiguity has no impact, since it amounts to an overall metric conformal factor. We also show that the Hamilton-Jacobi equation for light rays propagating in a plasma admits separability if the plasma frequency obeys a certain constraint. As an illustration, we compute the shadow and lensing of some spinning black holes obtained by the MNJA.

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arXiv2020

Quasinormal modes of hot, cold and bald Einstein-Maxwell-scalar black holes

Einstein-Maxwell-scalar models allow for different classes of black hole solutions, depending on the non-minimal coupling function $f(ϕ)$ employed, between the scalar field and the Maxwell invariant. Here, we address the linear mode stability of the black hole solutions obtained recently for a quartic coupling function, $f(ϕ)=1+αϕ^4$ [1]. Besides the bald Reissner-Nordström solutions, this coupling allows for two branches of scalarized black holes, termed cold and hot, respectively. For these three branches of black holes we calculate the spectrum of quasinormal modes. It consists of polar scalar-led modes, polar and axial electromagnetic-led modes, and polar and axial gravitational-led modes. We demonstrate that the only unstable mode present is the radial scalar-led mode of the cold branch. Consequently, the bald Reissner-Nordström branch and the hot scalarized branch are both mode-stable. The non-trivial scalar field in the scalarized background solutions leads to the breaking of the degeneracy between axial and polar modes present for Reissner-Nordström solutions. This isospectrality is only slightly broken on the cold branch, but it is strongly broken on the hot branch.

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arXiv2020

Tidal Love numbers of Proca stars

Proca stars (arXiv:1508.05395) are everywhere regular, asymptotically flat self-gravitating solitons composed of complex, massive vector bosons, forming a macroscopic, star-sized, Bose-Einstein condensate. They have been suggested as a classical, dynamical model of exotic compact objects, black hole mimickers and dark matter candidates. In spherical symmetry, they are qualitatively similar to their scalar cousins, the standard (scalar) boson stars in all respects studied so far. Here we study the tidal deformability and the quadrupolar tidal Love numbers, both electric-type and magnetic-type, of spherically symmetric Proca stars. The equations for the perturbations are derived and the numerical values of the Love numbers for some concrete background solutions are computed. We observe that both Love numbers are qualitatively similar to the ones of the scalar boson stars; in particular, the electric-type (magnetic-type) quadrupolar Love numbers are positive (negative) for Proca stars. Quantitatively, for the same compactness, the electric and magnetic Love numbers in the Proca case are closer (in magnitude) than in the scalar case, with the electric Love numbers having a slightly larger magnitude than the magnetic ones.

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arXiv2020

Rotating Axion Boson Stars

We construct and study rotating axion boson stars (RABSs). These are the spinning generalisations of the spherical gravitating solitons recently introduced in arXiv:1909.05515. RABSs are asymptotically flat, stationary, axially symmetric, everywhere regular solutions of the Einstein-Klein-Gordon theory, in the presence of a periodic scalar potential arising in models of axion-like particles. The potential is characterised by two parameters: the mass of the scalar field $m_a$ and the decay constant $f_a$. We present an overview of the solution space, for different values of $f_a$, and analyse some of their phenomenological properties. For large decay constants the solutions become identical to the standard spinning mini boson stars. For small decay constants, on the other hand, the solutions develop distinctive features. In particular, we analyse their compactness, the emergence of ergoregions, light rings and the distribution of stable and unstable equatorial timelike circular orbits, including the innermost stable circular orbit. We also establish the occurrence of violations of the strong energy condition for physical observers, for some RABSs. We observe some analogy between RABSs and spinning gravitating $Q$-balls.

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arXiv2020

Stationary scalar and vector clouds around Kerr-Newman black holes

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: $n$, the number of nodes in the radial direction; $\ell$, the orbital angular momentum; $j$, the total angular momentum; and $m_j$, 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.

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arXiv2020

Electromagnetic dual Einstein-Maxwell-scalar models

Electromagnetic duality is discussed in the context of Einstein-Maxwell-scalar (EMS) models including axionic-type couplings. This family of models introduces two non-minimal coupling functions $f(ϕ)$ and $g(ϕ)$, depending on a real scalar field $ϕ$. Interpreting the scalar field as a medium, one naturally defines constitutive relations as in relativistic non-linear electrodynamics. Requiring these constitutive relations to be invariant under the $SO(2)$ electromagnetic duality rotations of Maxwell's theory, defines 1-parameter, closed $\textit{duality orbits}$ in the space of EMS models, connecting different electromagnetic fields in "dual" models with different coupling functions, but leaving both the scalar field and the spacetime geometry invariant. This mapping works as a solution generating technique, extending any given solution of a specific model to a (different) solution for any of the dual models along the whole duality orbit. We illustrate this technique by considering the duality orbits seeded by specific EMS models wherein solitonic and black hole solutions are known. For dilatonic models, specific rotations are equivalent to $S$-duality.

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arXiv2020

Spherical electro-vacuum black holes with resonant, scalar $Q$-hair

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 $Q$-ball type potential for the scalar field, we dub these configurations $Q$-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, $Q$-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 $Q$-clouds around Schwarzschild and Reissner-Nordström BHs, showing there is always a mass gap. Then, we make the $Q$-clouds backreact, and construct fully non-linear solutions of the Einstein-Maxwell-gauged scalar system describing spherical, charged BHs with resonant, scalar $Q$-hair. Amongst other properties, we observe there is non-uniqueness of charged BHs in this model and the $Q$-hairy BHs can be entropically preferred over Reissner-Nordström, for the same charge to mass ratio; some $Q$-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.

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arXiv2020

Black holes with synchronised Proca hair: linear clouds and fundamental non-linear solutions

Recent studies have made key progress on the black hole/solitonic solutions of the Einstein-Proca system. Firstly, fully non-linear dynamical evolutions of the Kerr black hole superradiant instability, triggered by a Proca field, have shown the formation of a new equilibrium state, a spinning black hole with synchronised Proca hair. Secondly, non-linear evolutions of spinning Proca stars have established that they are dynamically stable, unlike their scalar cousins. Thirdy, separability of the Proca equation on the Kerr background has been achieved. Motivated by these results, in this paper we reconsider Kerr black holes with synchronised Proca hair. The separability of the Proca equation on the Kerr background allows us to examine the stationary Proca clouds in greater detail, in particular their dependence on the different quantum numbers. These stationary clouds occur at a set of existence lines in the Kerr parameter space, from which the black holes with synchronised Proca hair bifurcate. We construct the domain of existence of these black holes, comparing the fundamental states missed in the original study with the first excited states and with the cousin scalar model, giving illustrative examples of Kerr-like and non-Kerr-like BHs. In the vanishing event horizon limit, these hairy black holes connect to the fundamental states of spinning Proca stars, which include the dynamically stable solutions.

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arXiv2020

Stationary black holes and light rings

The ringdown and shadow of the astrophysically significant Kerr Black Hole (BH) are both intimately connected to a special set of bound null orbits known as Light Rings (LRs). Does it hold that a generic equilibrium BH must possess such orbits? In this letter we prove the following theorem. A stationary, axi-symmetric, asymptotically flat black hole spacetime in 1+3 dimensions, with a non-extremal, topologically spherical, Killing horizon admits, at least, one standard LR outside the horizon for each rotation sense. The proof relies on a topological argument and assumes $C^2$-smoothness and circularity, but makes no use of the field equations. The argument is also adapted to recover a previous theorem establishing that a horizonless ultra-compact object must admit an even number of non-degenerate LRs, one of which is stable.

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arXiv2020

Spinning black holes in shift-symmetric Horndeski theory

We construct spinning black holes (BHs) in shift-symmetric Horndeski theory. This is an Einstein-scalar-Gauss-Bonnet model wherein the (real) scalar field couples linearly to the Gauss-Bonnet curvature squared combination. The BH solutions constructed are stationary, axially symmetric and asymptotically flat. They possess a non-trivial scalar field outside their regular event horizon; thus they have scalar hair. The scalar "charge" is not, however, an independent macroscopic degree of freedom. It is proportional to the Hawking temperature, as in the static limit, wherein the BHs reduce to the spherical solutions found by Sotirou and Zhou. The spinning BHs herein are found by solving non-perturbatively the field equations, numerically. We present an overview of the parameter space of the solutions together with a study of their basic geometric and phenomenological properties. These solutions are compared with the spinning BHs in the Einstein-dilaton-Gauss-Bonnet model and the Kerr BH of vacuum General Relativity. As for the former, and in contrast with the latter, there is a minimal BH size and small violations of the Kerr bound. Phenomenological differences with respect to either the former or the latter, however, are small for illustrative observables, being of the order of a few percent, at most.

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arXiv2020

Einstein-Maxwell-scalar black holes: the hot, the cold and the bald

The phenomenon of spontaneous scalarisation of charged black holes (BHs) has recently motivated studies of various Einstein-Maxwell-scalar models. Within these models, different classes of BH solutions are possible, depending on the non-minimal coupling function $f(ϕ)$, between the scalar field and the Maxwell invariant. Here we consider the class wherein both the (bald) electrovacuum Reissner-Nordström (RN) BH and new scalarised BHs co-exist, and the former are never unstable against scalar perturbations. In particular we examine the model, within this subclass, with a quartic coupling function: $f(Φ) = 1+αΦ^4$. The domain of existence of the scalarised BHs, for fixed $α$, is composed of two branches. The first branch (cold scalarised BHs) is continuously connected to the extremal RN BH. The second branch (hot scalarised BHs) connects to the first one at the minimum value of the charge to mass ratio and it includes overcharged BHs. We then assess the perturbative stability of the scalarised solutions, focusing on spherical perturbations. On the one hand, cold scalarised BHs are shown to be unstable by explicitly computing growing modes. The instability is quenched at both endpoints of the first branch. On the other hand, hot scalarised BHs are shown to be stable by using the S-deformation method. Thus, in the spherical sector this model possesses two stable BH local ground states (RN and hot scalarised). We point out that the branch structure of BHs in this model parallels the one of BHs in five dimensional vacuum gravity, with [Myer-Perry BHs, fat rings, thin rings] playing the role of [RN, cold scalarised, hot scalarised] BHs.

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arXiv2020

EHT constraint on the ultralight scalar hair of the M87 supermassive black hole

Hypothetical ultralight bosonic fields will spontaneously form macroscopic bosonic halos around Kerr black holes, via superradiance, transferring part of the mass and angular momentum of the black hole into the halo. Such process, however, is only efficient if resonant: when the Compton wavelength of the field approximately matches the gravitational scale of the black hole. For a complex-valued field, the process can form a stationary, bosonic field-black hole equilibrium state - a black hole with synchronised hair. For sufficiently massive black holes, such as the one at the centre of the M87 supergiant elliptic galaxy, the hairy black hole can be robust against its own superradiant instabilities, within a Hubble time. Studying the shadows of such scalar hairy black holes, we constrain the amount of hair which is compatible with the Event Horizon Telescope (EHT) observations of the M87 supermassive black hole, assuming the hair is a condensate of ultralight scalar particles of mass $μ\sim 10^{-20}$ eV, as to be dynamically viable. We show the EHT observations set a weak constraint, in the sense that typical hairy black holes that could develop their hair dynamically, are compatible with the observations, when taking into account the EHT error bars and the black hole mass/distance uncertainty.

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arXiv2019

Lensing and shadow of a black hole surrounded by a heavy accretion disk

We consider a static, axially symmetric spacetime describing the superposition of a Schwarzschild black hole (BH) with a thin and heavy accretion disk. The BH-disk configuration is a solution of the Einstein field equations within the Weyl class. The disk is sourced by a distributional energy-momentum tensor and it is located at the equatorial plane. It can be interpreted as two streams of counter-rotating particles, yielding a total vanishing angular momentum. The phenomenology of the composed system depends on two parameters: the fraction of the total mass in the disk, $m$, and the location of the inner edge of the disk, $a$. We start by determining the sub-region of the space of parameters wherein the solution is physical, by requiring the velocity of the disk particles to be sub-luminal and real. Then, we study the null geodesic flow by performing backwards ray-tracing under two scenarios. In the first scenario the composed system is illuminated by the disk and in the second scenario the composed system is illuminated by a far-away celestial sphere. Both cases show that, as $m$ grows, the shadow becomes more prolate. Additionally, the first scenario makes clear that as $m$ grows, for fixed $a$, the geometrically thin disk appears optically enlarged, i.e., thicker, when observed from the equatorial plane. This is to due to light rays that are bent towards the disk, when backwards ray traced. In the second scenario, these light rays can cross the disk (which is assumed to be transparent) and may oscillate up to a few times before reaching the far away celestial sphere. Consequently, an almost equatorial observer sees different patches of the sky near the equatorial plane, as a chaotic "mirage". As $m\rightarrow 0$ one recovers the standard test, i.e., negligible mass, disk appearance.

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arXiv2019

Einstein and Eddington and the eclipse in Principe: Celebration and science 100 years after

On May 29, 1919, at Roça Sundy, Principe island, Eddington confirms Einstein's general relativity theory for the first time by photographing stars behind the obscured Sun during a total eclipse. History was made. At Sobral, Eddington's astronomer colleagues photograph the same eclipse and also conclude that light from distant stars suffers a deflection when passing by the gravitational field of the Sun, in accordance with general relativity. With the confirmation of general relativity, a theory of gravitation at a fundamental level, physics became, once and for all, relativist and its future was outlined. The first world war had finished a few months before and the deep wounds between nations were yet to heal. Science wanted to be above it all showing that people could be united by a common goal. This year, the 100 years of this achievement was commemorated with the scientific conference "From Einstein and Eddington to LIGO: 100 years of gravitational light deflection" in Principe to celebrate this landmark event. We report here on this conference of celebration.

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arXiv2019

The black hole fifty years after: Genesis of the name

Black holes are extreme spacetime deformations where even light is imprisoned. There is an extensive astrophysical evidence for the real and abundant existence of these prisons of matter and light in the Universe. Mathematically, black holes are described by solutions of the field equations of the theory of general relativity, the first of which was published in 1916 by Karl Schwarzschild. Another highly relevant solution, representing a rotating black hole, was found by Roy Kerr in 1963. It was only much after the publication of the Schwarzschild solution, however, that the term black hole was employed to describe these objects. Who invented it? Conventional wisdom attributes the origin of the term to the prominent North American physicist John Wheeler who first adopted it in a general audience article published in 1968. This, however, is just one side of a story that begins two hundred years before in an Indian prison colloquially known as the Black Hole of Calcutta. Robert Dicke, also a distinguished physicist and colleague of Wheeler at Princeton University, aware of the prison's tragedy began, around 1960, to compare gravitationally completely collapsed stars to the black hole of Calcutta. The whole account thus suggests reconsidering who indeed coined the name black hole and commends acknowledging its definitive birth to a partnership between Wheeler and Dicke.

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