arXiv subjects

Eugen Radu

Publications and source records attributed to Eugen Radu.

At least 163 records · Page 9Linked to original sources

arXiv2015

Static black holes with axial symmetry in asymptotically AdS$_4$ spacetime

The known static electro-vacuum black holes in a globally AdS$_4$ background have an event horizon which is geometrically a round sphere. In this work we argue that the situation is different in models with matter fields possessing an explicit dependence on the azimuthal angle $φ$, which, however, does not manifest at the level of the energy-momentum tensor. As a result, the full solutions are axially symmetric only, possessing a single (timelike) Killing vector field. Explicit examples of such static black holes are constructed in Einstein--(complex) scalar field and Einstein--Yang-Mills theories. The basic properties of these solutions are discussed, looking for generic features. For example, we notice that the horizon has an oblate spheroidal shape for solutions with a scalar field and a prolate one for black holes with Yang-Mills fields. The deviation from sphericity of the horizon geometry manifests itself in the holographic stress-tensor. Finally, based on the results obtained in the probe limit, we conjecture the existence in the Einstein-Maxwell theory of static black holes with axial symmetry only.

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

Anti-de-Sitter regular electric multipoles: towards Einstein-Maxwell-AdS solitons

We discuss electrostatics in Anti-de-Sitter ($AdS$) spacetime, in global coordinates. We observe that the multipolar expansion has two crucial differences to that in Minkowski spacetime. First, there are everywhere regular solutions, with finite energy, for every multipole moment except for the monopole. Second, all multipole moments decay with the same inverse power of the areal radius, $1/r$, as spatial infinity is approached. The first observation suggests there may be regular, self-gravitating, Einstein-Maxwell solitons in $AdS$ spacetime. The second observation, renders a Lichnerowicz-type no-soliton theorem inapplicable. Consequently, we suggest Einstein-Maxwell solitons exist in $AdS$, and we support this claim by computing the first order metric perturbations sourced by test electric field multipoles, which are obtained analytically in closed form.

gr-qc↗

arXiv2015

Radially excited rotating black holes in Einstein-Maxwell-Chern-Simons theory

Rotating black holes in Einstein-Maxwell-Chern-Simons theory possess remarkable features, when the Chern-Simons coupling constant reaches a critical value. Representing single asymptotically flat black holes with horizons of spherical topology, they exhibit non-uniqueness. In particular, there even exist extremal and non-extremal black holes with the same sets of global charges. Both extremal and non-extremal black holes form sequences of radially excited solutions, that can be labeled by the node number of the magnetic gauge potential function. The extremal Reissner-Nordström solution is no longer always located on the boundary of the domain of existence of these black holes, and it neither remains the single extremal solution with vanishing angular momentum. Instead a whole sequence of rotating extremal $J=0$ solutions is present, whose mass converges towards the mass of the Reissner-Nordström solution. These radially excited extremal solutions are all associated with the same near horizon solution. Moreover, there are near horizon solutions that are not realized as global solutions.

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↗

arXiv2015

Myers-Perry black holes with scalar hair and a mass gap: unequal spins

We construct rotating boson stars and Myers-Perry black holes with scalar hair (MPBHsSH) as fully non-linear solutions of five dimensional Einstein gravity minimally coupled to a complex, massive scalar field. The MPBHsSH are, in general, regular on and outside the horizon, asymptotically flat, and possess angular momentum in a single rotation plane. They are supported by rotation and have no static limit. Such hairy BHs may be thought of as bound states of boson stars and singly spinning, vacuum MPBHs and inherit properties of both these building blocks. When the horizon area shrinks to zero, the solutions reduce to (in a single plane) rotating boson stars; but the extremal limit also yields a zero area horizon, as for singly spinning MPBHs. Similarly to the case of equal angular momenta, and in contrast to Kerr black holes with scalar hair, singly spinning MPBHsSH are disconnected from the vacuum black holes, due to a mass gap. We observe that for the general case, with two unequal angular momenta, the equilibrium condition for the existence of MPBHsSH is $w=m_1Ω_1+m_2Ω_2$, where $Ω_i$ are the horizon angular velocities in the two independent rotation planes and $w,m_i$, $i=1,2$, are the scalar field's frequency and azimuthal harmonic indices.

gr-qc↗

arXiv2015

Construction and physical properties of Kerr black holes with scalar hair

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 (arXiv:1403.2757). 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.

gr-qc↗

arXiv2015

Thermodynamic properties of asymptotically anti-de Sitter black holes in d=4 Einstein-Yang-Mills theory

We investigate the thermodynamics of spherically symmetric black hole solutions in a four-dimensional Einstein--Yang-Mills-SU(2) theory with a negative cosmological constant. Special attention is paid to configurations with a unit magnetic charge. We find that a set of Reissner-Nordström--Anti-de Sitter black holes can become unstable to forming non-Abelian hair. However, the hairy black holes are never thermodynamically favoured over the full set of abelian monopole solutions. The thermodynamics of the generic configurations possessing a noninteger magnetic charge is also discussed.

hep-th↗

arXiv2015

Charged isotropic non-Abelian dyonic black branes

We construct black holes with a Ricci flat horizon in Einstein--Yang-Mills theory with a negative cosmological constant, which approach asymptotically an AdS$_d$ spacetime background (with $d\geq 4$). These solutions are isotropic, $i.e.$ all space directions in a hypersurface of constant radial and time coordinates are equivalent, and possess both electric and magnetic fields. We find that the basic properties of the non-Abelian solutions are similar to those of the dyonic isotropic branes in Einstein-Maxwell theory (which, however, exist in even spacetime dimensions only). These black branes possess a nonzero magnetic field strength on the flat boundary metric, which leads to a divergent mass of these solutions, as defined in the usual way. However, a different picture is found for odd spacetime dimensions, where a non-Abelian Chern-Simons term can be incorporated in the action. This allows for black brane solutions with a magnetic field which vanishes asymptotically.

gr-qc↗

arXiv2015

Acoustic clouds: standing sound waves around a black hole analogue

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.

gr-qc↗

arXiv2014

Black ringoids: spinning balanced black objects in $d\geq 5$ dimensions -- the codimension-two case

We propose a general framework for the study of asymptotically flat black objects with $k+1$ equal magnitude angular momenta in $d\geq 5$ spacetime dimensions (with $0\leq k\leq \big[\frac{d-5}{2} \big]$). In this approach, the dependence on all angular coordinates but one is factorized, which leads to a codimension-two problem. This framework can describe black holes with spherical horizon topology, the simplest solutions corresponding to a class of Myers-Perry black holes. A different set of solutions describes balanced black objects with $S^{n+1} \times S^{2k+1}$ horizon topology. The simplest members of this family are the black rings $(k=0)$. The solutions with $k>0$ are dubbed $black~ringoids$. Based on the nonperturbative numerical results found for several values of $(n,k)$, we propose a general picture for the properties and the phase diagram of these solutions and the associated black holes with spherical horizon topology: $n=1$ black ringoids repeat the $k=0$ pattern of black rings and Myers-Perry black holes in 5 dimensions, whereas $n>1$ black ringoids follow the pattern of higher dimensional black rings associated with `pinched' black holes and Myers-Perry black holes.

gr-qc↗

arXiv2014

Kerr-Newman scalar clouds

Massive complex scalar fields can form bound states around Kerr black holes. These bound states -- dubbed scalar clouds -- are generically non-zero and finite on and outside the horizon; they decay exponentially at spatial infinity, have a real frequency and are specified by a set of integer "quantum" numbers (n,l,m). For a specific set of these numbers, the clouds are only possible along a 1-dimensional subset of the 2-dimensional parameter space of Kerr black holes, called an existence line. In this paper we make a thorough investigation of the scalar clouds due to neutral (charged) scalar fields around Kerr(-Newman) black holes. We present the location of the existence lines for a variety of quantum numbers, their spatial representation and compare analytic approximation formulas in the literature with our exact numerical results, exhibiting a sometimes remarkable agreement.

gr-qc↗

arXiv2014

Non-linear Q-clouds around Kerr black holes

Q-balls are regular extended `objects' that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr) black holes, as non-linear bound states of a test scalar field. We dub such configurations Q-clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces - existence lines - of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q-clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q-cloud reduces to a linear cloud. Thus, Q-clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q-clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family.

gr-qc↗

arXiv2014

Non-Abelian fields in AdS$_4$ spacetime: axially symmetric, composite configurations

We construct new finite energy regular solutions in Einstein-Yang-Mills-SU(2) theory. They are static, axially symmetric and approach at infinity the anti-de Sitter spacetime background. These configurations are characterized by a pair of integers $(m, n)$, where $m$ is related to the polar angle and $n$ to the azimuthal angle, being related to the known flat space monopole-antimonopole chains and vortex rings. Generically, they describe composite configurations with several individual components, possesing a nonzero magnetic charge, even in the absence of a Higgs field. Such Yang-Mills configurations exist already in the probe limit, the AdS geometry supplying the attractive force needed to balance the repulsive force of Yang-Mills gauge interactions. The gravitating solutions are constructed by numerically solving the elliptic Einstein-DeTurck--Yang-Mills equations. The variation of the gravitational coupling constant $α$ reveals the existence of two branches of gravitating solutions which bifurcate at some critical value of $α$. The lower energy branch connects to the solutions in the global AdS spacetime, while the upper branch is linked to the generalized Bartnik-McKinnon solutions in asymptotically flat spacetime. Also, a spherically symmetric, closed form solution is found as a perturbation around the globally anti-de Sitter vacuum state.

gr-qc↗

arXiv2014

Myers-Perry black holes with scalar hair and a mass gap

We construct a family of asymptotically flat, rotating black holes with scalar hair and a regular horizon, within five dimensional Einstein's gravity minimally coupled to a complex, massive scalar field doublet. These solutions are supported by rotation and have no static limit. They are described by their mass $M$, two equal angular momenta $J_1=J_2\equiv J$ and a conserved Noether charge $Q$, measuring the scalar hair. For vanishing horizon size the solutions reduce to five dimensional boson stars. In the limit of vanishing Noether charge density, the scalar field becomes point-wise arbitrarily small and the geometry becomes, locally, arbitrarily close to that of a specific set of Myers-Perry black holes (MPBHs); but there remains a global difference with respect to the latter, manifest in a finite mass gap. Thus, the scalar hair never becomes a linear perturbation of MPBHs. This is a qualitative difference when compared to Kerr black holes with scalar hair~\cite{Herdeiro:2014goa}. Whereas the existence of the latter can be anticipated in linear theory, from the existence of scalar bound states on the Kerr geometry (i.e. scalar clouds), the hair of these MPBHs is intrinsically non-linear.

gr-qc↗

arXiv2014

Generalized dyons and magnetic dipoles: the issue of angular momentum

It is known that a non-Abelian magnetic monopole cannot rotate globally (although it may possess a nonzero angular momentum density). At the same time, the total angular momentum of a magnetic dipole equals the electric charge. In this work we question the generality of these results by considering a number of generalizations of the Georgi-Glashow model. We study two different types of finite energy, regular configurations: solutions with net magnetic charge and monopole-antimonopole pairs with zero net magnetic charge. These configurations are endowed with an electric charge and carry also a nonvanishing angular momentum density. However, we argue that the qualitative results found in the Georgi-Glashow model are generic and thus a magnetic monopole cannot spin as long as the matter fields feature the usual "monopole" asymptotic behaviour independently of the dynamics of the model. A study of the properties of the dyons and magnetic dipoles in some generalizations of the Georgi-Glashow model supplemented with higher order Skyrme-like terms in the gauge curvature and Higgs fields is given quantitatively.

hep-th↗