arXiv subjects

Carlos Herdeiro

Publications and source records attributed to Carlos Herdeiro.

At least 91 records · Page 5Linked to original sources

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

Testing the nonlinear stability of Kerr-Newman black holes

The nonlinear stability of Kerr-Newman black holes (KNBHs) is investigated by performing numerical simulations within the full Einstein-Maxwell theory. We take as initial data a KNBH with mass $M$, angular momentum to mass ratio $a$ and charge $Q$. Evolutions are performed to scan this parameter space within the intervals $0\le a/M\le 0.994$ and $0\le Q/M\le 0.996$, corresponding to an extremality parameter $a/a_{\rm max}$ ($a_{\rm max} \equiv \sqrt{M^2-Q^2}$) ranging from $0$ to $0.995$. These KNBHs are evolved, together with a small bar-mode perturbation, up to a time of order $120M$. Our results suggest that for small $Q/a$, the quadrupolar oscillation modes depend solely on $a/a_{\rm max}$, a universality also apparent in previous perturbative studies in the regime of small rotation. Using as a stability criterion the absence of significant relative variations in the horizon areal radius and BH spin, we find no evidence for any developing instability.

gr-qc↗

arXiv2014

Radiation from a $D$-dimensional collision of shock waves: proof of first order formula and angular factorisation at all orders

In two previous papers we have computed the inelasticity $ε$ in a head-on collision of two $D$-dimensional Aichelburg-Sexl shock waves, using perturbation theory to calculate the geometry in the future light-cone of the collision. The first order result, obtained as an accurate numerical fit, yielded the remarkably simple formula $ε_{\rm 1st\, order} = 1/2 - 1/D$. Here we show, analytically, that this result is exact in first order perturbation theory. Moreover, we clarify the relation between perturbation theory and an angular series of the inelasticity's angular power around the symmetry axis of the collision $(θ= 0,π)$. To establish these results, firstly, we show that at null infinity the angular dependence factorises order by order in perturbation theory, as a result of a hidden symmetry. Secondly, we show that a consistent truncation of the angular series in powers of $\sin^2 θ$ at some order $O(n)$ requires knowledge of the metric perturbations up to $O(n+1)$. In particular, this justifies the isotropy assumption used in first order perturbation theory. We then compute, analytically, all terms that contribute to the inelasticity and depend linearly on the initial conditions (surface terms), including second order contributions.

hep-th↗

arXiv2014

PPN expansion and FRW scalar perturbations in n-DBI gravity

n-DBI gravity 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 look for observational consequences of this mode in two setups. Firstly, we compute the parametrized post-Newtonian (PPN) expansion of the metric to first post-Newtonian order. Surprisingly, we find that the PPN parameters are exactly the same as in General Relativity (GR), and no preferred-frame effects are produced. In particular this means that n-DBI gravity is consistent with all GR solar system experimental tests. We discuss the origin of such degeneracy between n-DBI gravity and GR, and suggest it may also hold in higher post-Newtonian order. Secondly, we study gravitational scalar perturbations of a Friedmann-Robertson-Walker space-time with a cosmological constant $Λ\geq 0$. In the case of de Sitter space, we show that the scalar mode grows as the universe expands and, in contrast with a canonical scalar field coupled to GR, it does not freeze on super horizon scales.

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

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

Ergo-spheres, ergo-tori and ergo-Saturns for Kerr black holes with scalar hair

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 remarkable ergo-surfaces, should also arise for other rotating `hairy' black holes.

gr-qc↗

arXiv2014

Marginal scalar and Proca clouds around Reissner-Nordström black holes

Massive scalar test fields around Kerr black holes can form quasi-bound states with complex frequencies. Some of these states decay in time, but some others -- in the superradiant regime -- grow, causing a superradiant instability. Precisely at the threshold between decaying and growing modes, there exist bound states with real frequency, known as scalar clouds. Fully non-linear counterparts of these clouds have been shown to yield Kerr black holes with scalar hair. Here, we consider massive, (electrically) charged, test scalar and Proca fields on the background of Reissner-Nordström black holes. By computing the quasi-bound state frequencies, we establish that no such states exist in the superradiant regime for the Proca field -- a similar behavior to that known for scalar fields. But decaying quasi-bound states with an arbitrarily small imaginary part of the frequency exist and thus which are arbitrarily long lived. In the limit of vanishing imaginary part of the frequency, the field does not trivialize and we dub the corresponding configurations as marginal (charged) scalar or Proca clouds, since they are only marginally bound. We comment on the possible existence of non-linear counterparts to these marginal clouds.

gr-qc↗

arXiv2014

Higher dimensional Numerical Relativity: code comparison

The nonlinear behavior of higher dimensional black hole spacetimes is of interest in several contexts, ranging from an understanding of cosmic censorship to black hole production in high-energy collisions. However, nonlinear numerical evolutions of higher dimensional black hole spacetimes are tremendously complex, involving different diagnostic tools and "dimensional reduction methods". In this work we compare two different successful codes to evolve Einstein's equations in higher dimensions, and show that the results of such different procedures agree to numerical precision, when applied to the collision from rest of two equal-mass black holes. We calculate the total radiated energy to be E/M=9x10^{-4} in five dimensions and E/M=8.1x10^{-4} in six dimensions.

gr-qc↗

arXiv2014

Superradiant instabilities in a $D$-dimensional small Reissner-Nordström-Anti-de Sitter black hole

We investigate the superradiant instability for a charged scalar field in a $D$-dimensional small Reissner-Nordström-Anti-de Sitter (RN-AdS) black hole. Firstly, we solve the charged Klein-Gordon equation analytically by a matching method. We show that the general $D$-dimensional quasinormal frequencies depend on the relation between the angular momentum quantum number, $\ell$, and $D$. When $\ell$ is a (non-negative) integer multiple of $D-3$, i.e $\ell=p(D-3)$, we find an analytical quasinormal frequency formula adding a purely imaginary correction to the AdS normal frequencies. This is the case for all $\ell$ modes in $D=4$. For general $D$ there are two more cases: i) when $\ell$ obeys $\ell=(p+\frac{1}{2})(D-3)$, which can occur for odd $D$, we observe that the matching method fails, since the near and far region solutions have different functional dependences; ii) for all other cases, the analytical quasinormal frequency formula gives a complex correction to the AdS normal frequencies. Secondly, we perform a numerical calculation which confirms the analytical formulas obtained with the matching method and allows us to explore the case where that method failed. In the latter case, as in the former, we verify that all $\ell$ modes for all $D$ may become superradiant, which contradicts a previous claim in the literature.

gr-qc↗

arXiv2014

Collisions of oppositely charged black holes

The first fully non-linear numerical simulations of colliding charged black holes in D=4 Einstein-Maxwell theory were recently reported arXiv:1205.1063. These collisions were performed for black holes with equal charge-to-mass ratio, for which initial data can be found in closed analytic form. Here we generalize the study of collisions of charged black holes to the case of unequal charge-to-mass ratios. We focus on oppositely charged black holes, as to maximize acceleration-dependent effects. As |Q|/M increases from 0 to 0.99, we observe that the gravitational radiation emitted increases by a factor of ~ 2.7; the electromagnetic radiation emission becomes dominant for |Q|/M >~ 0.37 and at |Q|/M=0.99 is larger, by a factor of ~ 5.8, than its gravitational counterpart. We observe that these numerical results exhibit a precise and simple scaling with the charge. Furthermore, we show that the results from the numerical simulations are qualitatively captured by a simple analytic model that computes the electromagnetic dipolar radiation and the gravitational quadrupolar radiation of two non-relativistic interacting particles in Minkowski spacetime.

gr-qc↗

arXiv2013

Radiation from a D-dimensional collision of shock waves: higher order set up and perturbation theory validity

The collision of two D-dimensional, ultra-relativistic particles, described in General Relativity as Aichelberg-Sexl shock waves, is inelastic. In first order perturbation theory, the fraction of the initial centre of mass energy radiated away was recently shown to be 1/2 - 1/D. Here, we extend the formalism to higher orders in perturbation theory, and derive a general expression to extract the inelasticity, valid non-perturbatively, based on the Bondi mass loss formula. Then, to clarify why perturbation theory captures relevant physics of a strong field process in this problem, we provide one variation of the problem where the perturbative framework breaks down: the collision of ultra-relativistic charged particles. The addition of charge, and the associated repulsive nature of the source, originates an extra radiation burst, which we argue to be an artifact of the perturbative framework, veiling the relevant physics.

hep-th↗

arXiv2013

Hawking radiation for a Proca field in D dimensions II: charged field in a brane charged black hole

We generalise our first analysis of the wave equation for a massive vector boson in the background of a D-dimensional Schwarzschild black hole, by adding charge both to the field and the black hole, on the 3+1 dimensional Standard Model brane. A detailed numerical study is performed to obtain the transmission factor for the coupled (as well as decoupled) system of equations describing the Proca field modes, varying the angular momentum number, mass, charge and space-time dimensions. A qualitatively new feature arising from the introduction of charge is the appearance of superradiant modes, which we investigate. We then compute the Hawking fluxes, and analyse the effect of the charge. In particular we observe an inverted charge splitting effect for small energies and for two or more extra dimensions. For neutral fields, we compare the emission of massive particles with spins up to one and also compare the Proca bulk-to-brane ratio of energy emission, showing that, as for a scalar field, most of the energy is emitted on the brane.

gr-qc↗

arXiv2013

n-DBI Gravity in a nutshell

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.

gr-qc↗

arXiv2013

n-DBI gravity, maximal slicing and the Kerr geometry

Recently, in arXiv:1110.0832, we have established that solutions of Einstein's gravity admitting foliations with a certain geometric condition are also solutions of n-DBI gravity, arXiv:1109.1468. Here we observe that, in vacuum, the required geometric condition is fulfilled by the well known maximal slicing, often used in numerical relativity. As a corollary, we establish that the Kerr geometry is a solution of n-DBI gravity in the foliation adapted to Boyer-Lindquist coordinates.

gr-qc↗

arXiv2012

Collisions of charged black holes

We perform fully non-linear numerical simulations of charged-black-hole collisions, described by the Einstein-Maxwell equations, and contrast the results against analytic expectations. We focus on head-on collisions of non-spinning black holes, starting from rest and with the same charge to mass ratio, Q/M. The addition of charge to black holes introduces a new interesting channel of radiation and dynamics, most of which seem to be captured by Newtonian dynamics and flat-space intuition. The waveforms can be qualitatively described in terms of three stages; (i) an infall phase prior to the formation of a common apparent horizon; (ii) a nonlinear merger phase which corresponds to a peak in gravitational and electromagnetic energy; (iii) the ringdown marked by an oscillatory pattern with exponentially decaying amplitude and characteristic frequencies that are in good agreement with perturbative predictions. We observe that the amount of gravitational-wave energy generated throughout the collision decreases by about three orders of magnitude as the charge-to-mass ratio Q/M is increased from 0 to 0.98. We interpret this decrease as a consequence of the smaller accelerations present for larger values of the charge. In contrast, the ratio of energy carried by electromagnetic to gravitational radiation increases, reaching about 22% for the maximum Q/M ratio explored, which is in good agreement with analytic predictions.

gr-qc↗

arXiv2012

On the scalar graviton in n-DBI gravity

n-DBI gravity is a gravitational theory which yields near de Sitter inflation spontaneously at the cost of breaking Lorentz invariance by a preferred choice of foliation. We show that this breakdown endows n-DBI gravity with one extra physical gravitational degree of freedom: a scalar graviton. Its existence is established by Dirac's theory of constrained systems. Firstly, studying scalar perturbations around Minkowski space-time, we show that there exists one scalar degree of freedom and identify it in terms of the metric perturbations. Then, a general analysis is made in the canonical formalism, using ADM variables. It is useful to introduce an auxiliary scalar field, which allows recasting n-DBI gravity in an Einstein-Hilbert form but in a Jordan frame. Identifying the constraints and their classes we confirm the existence of an extra degree of freedom in the full theory, besides the two usual tensorial modes of the graviton. We then argue that, unlike the case of (the original proposal for) Horava-Lifschitz gravity, there is no evidence that the extra degree of freedom originates pathologies, such as vanishing lapse, instabilities and strong self-coupling at low energy scales.

hep-th↗