arXiv subjects

Roberto Emparan

Publications and source records attributed to Roberto Emparan.

At least 55 records · Page 3Linked to original sources

arXiv2019

Exotic compact objects with soft hair

Motivated by the lack of a general parametrization for exotic compact objects, we construct a class of perturbative solutions valid for small (but otherwise generic) multipolar deviations from a Schwarzschild metric in general relativity. We introduce two classes of exotic compact objects, with "soft" and "hard" hair, for which the curvature at the surface is respectively comparable to or much larger than that at the corresponding black-hole horizon. We extend the Hartle-Thorne formalism to relax the assumption of equatorial symmetry and to include deformations induced by multipole moments higher than the spin, thus constructing the most general, axisymmetric quasi-Schwarzschild solution to Einstein's vacuum equations. We explicitly construct several particular solutions of objects with soft hair, which might be useful for tests of quasi-black-hole metrics, and also to study deformed neutron stars. We show that the more compact a soft exotic object is, the less hairy it will be. All its multipole moments can approach their corresponding Kerr values only in two ways as their compactness increases: either logarithmically (or faster) if the moments are spin-induced, or linearly (or faster) otherwise. Our results suggest that it is challenging (but possibly feasible with next-generation gravitational-wave detectors) to distinguish Kerr black holes from a large class of ultracompact exotic objects on the basis of their different multipolar structure.

gr-qc↗

arXiv2019

Black holes, gravitational waves and fundamental physics: a roadmap

The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress.

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arXiv2018

Charged rotating black holes in higher dimensions

We use a recent implementation of the large $D$ expansion in order to construct the higher-dimensional Kerr-Newman black hole and also new charged rotating black bar solutions of the Einstein-Maxwell theory, all with rotation along a single plane. We describe the space of solutions, obtain their quasinormal modes, and study the appearance of instabilities as the horizons spread along the plane of rotation. Generically, the presence of charge makes the solutions less stable. Instabilities can appear even when the angular momentum of the black hole is small, as long as the charge is sufficiently large. We expect that, although our study is performed in the limit $D\to\infty$, the results provide a good approximation for charged rotating black holes at finite $D\geq 6$.

hep-th↗

arXiv2018

Rotating black holes and black bars at large D

We propose and demonstrate a new and efficient approach to investigate black hole dynamics in the limit of large number of dimensions $D$. The basic idea is that an asymptotically flat black brane evolving under the Gregory-Laflamme instability forms lumps that closely resemble a localized black hole. In this manner, the large-$D$ effective equations for extended black branes can be used to study localized black holes. We show that these equations have exact solutions for black-hole-like lumps on the brane, which correctly capture the main properties of Schwarzschild and Myers-Perry black holes at large $D$, including their slow quasinormal modes and the ultraspinning instabilities (axisymmetric or not) at large angular momenta. Furthermore, we obtain a novel class of rotating `black bar' solutions, which are stationary when $D\to\infty$, and are long-lived when $D$ is finite but large, since their gravitational wave emission is strongly suppressed. The leading large $D$ approximation reproduces to per-cent level accuracy previous numerical calculations of the bar-mode growth rate in $D=6,7$.

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arXiv2018

Black hole fusion in the extreme mass ratio limit

We present a simple, general, and accurate construction of the event horizons for the fusion of two neutral, rotating black holes with arbitrary orientation and values of their spins, in the extreme mass ratio limit where one black hole is much larger than the other. We compute several parameters that characterize the fusion and investigate their dependence on the black hole spin and orientation axis. We also exhibit and study the appearance of transient toroidal topology of the horizon. An earlier conjecture about universal critical exponents before and after an axisymmetric pinch is proven.

gr-qc↗

arXiv2017

Geometric polarization of plasmas and Love numbers of AdS black branes

We use AdS/CFT holography to study how a strongly-coupled plasma polarizes when the geometry where it resides is not flat. We compute the linear-response polarization coefficients, which are directly related to the static two-point correlation function of the stress-energy tensor. In the gravitational dual description, these parameters correspond to the tidal deformation coefficients---the Love numbers---of a black brane. We also compute the coefficients of static electric polarization of the plasma.

hep-th↗

arXiv2016

Hydro-elastic Complementarity in Black Branes at large D

We obtain the effective theory for the non-linear dynamics of black branes---both neutral and charged, in asymptotically flat or Anti-deSitter spacetimes---to leading order in the inverse-dimensional expansion. We find that black branes evolve as viscous fluids, but when they settle down they are more naturally viewed as solutions of an elastic soap-bubble theory. The two views are complementary: the same variable is regarded in one case as the energy density of the fluid, in the other as the deformation of the elastic membrane. The large-D theory captures finite-wavelength phenomena beyond the conventional reach of hydrodynamics. For asymptotically flat charged black branes (either Reissner-Nordstrom or p-brane-charged black branes) it yields the non-linear evolution of the Gregory-Laflamme instability at large D and its endpoint at stable non-uniform black branes. For Reissner-Nordstrom AdS black branes we find that sound perturbations do not propagate (have purely imaginary frequency) when their wavelength is below a certain charge-dependent value. We also study the polarization of black branes induced by an external electric field.

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arXiv2016

Exact Event Horizon of a Black Hole Merger

We argue that the event horizon of a binary black hole merger, in the extreme-mass-ratio limit where one of the black holes is much smaller than the other, can be described in an exact analytic way. This is done by tracing in the Schwarzschild geometry a congruence of null geodesics that approaches a null plane at infinity. Its form can be given explicitly in terms of elliptic functions, and we use it to analyze and illustrate the time-evolution of the horizon along the merger. We identify features such as the line of caustics at which light rays enter the horizon, and the critical point at which the horizons touch. We also compute several quantities that characterize these aspects of the merger.

gr-qc↗

arXiv2015

Evolution and endpoint of the black string instability: Large D solution

We derive a simple set of non-linear, (1+1)-dimensional partial differential equations that describe the dynamical evolution of black strings and branes to leading order in the expansion in the inverse of the number of dimensions D. These equations are easily solved numerically. Their solution shows that thin enough black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to stable non-uniform black strings. This proves an earlier conjecture about the endpoint of the instability of black strings in a large enough number of dimensions. If the initial black string is very thin, the final configuration is highly non-uniform and resembles a periodic array of localized black holes joined by short necks. We also present the equations that describe the non-linear dynamics of Anti-deSitter black branes at large D.

hep-th↗

arXiv2015

Effective theory of Black Holes in the 1/D expansion

The gravitational field of a black hole is strongly localized near its horizon when the number of dimensions D is very large. In this limit, we can effectively replace the black hole with a surface in a background geometry (eg Minkowski or Anti-deSitter space). The Einstein equations determine the effective equations that this 'black hole surface' (or membrane) must satisfy. We obtain them up to next-to-leading order in 1/D for static black holes of the Einstein-(A)dS theory. To leading order, and also to next order in Minkowski backgrounds, the equations of the effective theory are the same as soap-film equations, possibly up to a redshift factor. In particular, the Schwarzschild black hole is recovered as a spherical soap bubble. Less trivially, we find solutions for 'black droplets', ie black holes localized at the boundary of AdS, and for non-uniform black strings.

hep-th↗

arXiv2015

Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion

We use the inverse-dimensional expansion to compute analytically the frequencies of a set of quasinormal modes of static black holes of Einstein-(Anti-)de Sitter gravity, including the cases of spherical, planar or hyperbolic horizons. The modes we study are decoupled modes localized in the near-horizon region, which are the ones that capture physics peculiar to each black hole (such as their instabilities), and which in large black holes contain hydrodynamic behavior. Our results also give the unstable Gregory-Laflamme frequencies of Ricci-flat black branes to two orders higher in 1/D than previous calculations. We discuss the limits on the accuracy of these results due to the asymptotic but not convergent character of the 1/D expansion, which is due to the violation of the decoupling condition at finite D. Finally, we compare the frequencies for AdS black branes to calculations in the hydrodynamic expansion in powers of the momentum k. Our results extend up to k^9 for the sound mode and to k^8 for the shear mode.

hep-th↗

arXiv2014

Bumpy black holes

We study six-dimensional rotating black holes with bumpy horizons: these are topologically spherical, but the sizes of symmetric cycles on the horizon vary non-monotonically with the polar angle. We construct them numerically for the first three bumpy families, and follow them in solution space until they approach critical solutions with localized singularities on the horizon. We find strong evidence of the conical structures that have been conjectured to mediate the transitions to black rings, to black Saturns, and to a novel class of bumpy black rings. For a different, recently identified class of bumpy black holes, we find evidence that this family ends in solutions with a localized singularity that exhibits apparently universal properties, and which does not seem to allow for transitions to any known class of black holes.

hep-th↗

arXiv2014

Decoupling and non-decoupling dynamics of large D black holes

The limit of large number of dimensions localizes the gravitational field of a black hole in a well-defined region near the horizon. The perturbative dynamics of the black hole can then be characterized in terms of states in the near-horizon geometry. We investigate this by computing the spectrum of quasinormal modes of the Schwarzschild black hole in the 1/D expansion, which we find splits into two classes. Most modes are non-decoupled modes: non-normalizable states of the near-horizon geometry that straddle between the near-horizon zone and the asymptotic zone. They have frequency of order D/r_0 (with r_0 the horizon radius), and are also present in a large class of other black holes. There also exist a much smaller number of decoupled modes: normalizable states of the near-horizon geometry that are strongly suppressed in the asymptotic region. They have frequency of order 1/r_0, and are specific of each black hole. Our results for their frequencies are in excellent agreement with numerical calculations, in some cases even in D=4.

hep-th↗

arXiv2014

Instability of rotating black holes: large D analysis

We study the stability of odd-dimensional rotating black holes with equal angular momenta by performing an expansion in the inverse of the number of dimensions D. Universality at large $D$ allows us to calculate analytically the complex frequency of quasinormal modes to next-to-leading order in the expansion. We identify the onset of non-axisymmetric, bar-mode instabilities at a specific finite rotation, and axisymmetric instabilities at larger rotation. The former occur at the threshold where the modes become superradiant, and before the ultraspinning regime is reached. Our results fully confirm the picture found in numerical studies, with very good quantitative agreement. We extend the analysis to the same class of black holes in Anti-deSitter space, and find the same qualitative features. We also discuss the appearance at high frequencies of the universal set of (stable) quasinormal modes.

hep-th↗

arXiv2014

Effective hydrodynamics of black D3-branes

The long-wavelength effective field theory of world-volume fluctuations of black D3-branes is shown to be a hydrodynamical system to leading order in a gradient expansion. We study the system on a fiducial `cutoff' surface: the fluctuating geometry imprints its dynamics on the surface via an induced stress tensor whose conservation encapsulates the hydrodynamical description. For a generic non-extremal D3-brane, as we move our cutoff surface from the asymptotically flat near-boundary region to the near-horizon region, this hydrodynamical system interpolates between a non-conformal relativistic fluid and a non-relativistic incompressible fluid. We also consider the dependence on the deviation from extremality of the D3-branes. In the near-extremal case we recover the description in terms of a conformal relativistic fluid encountered in the AdS/CFT context. We argue that this system allows us therefore to explore the various connections that have hitherto been suggested relating the dynamics of gravitational systems and fluid dynamics. In particular, we go on to show that the blackfold effective field theory approach allows us to capture this hydrodynamical behaviour and moreover subsumes the constructions encountered in the fluid/gravity correspondence and the black hole membrane paradigm, providing thereby a universal language to explore the effective dynamics of black branes.

hep-th↗

arXiv2014

Universal quasinormal modes of large D black holes

We show that in the limit where the number of spacetime dimensions D grows to infinity a very large class of black holes (including non-extremal, static, asymptotically flat ones, with any number of gauge-field charges, possibly coupled to dilatons) possess a universal set of quasinormal modes whose complex frequencies depend only on the horizon radius and no other black hole parameters. The damping ratio of these modes vanishes like $D^{-2/3}$, so they are almost normal modes, or 'quasi-particle' excitations of the black hole. The structure responsible for the existence of these modes at large D is also present very generally in other black holes.

hep-th↗

arXiv2013

Holographic superconductivity in the large D expansion

We study holographic superconductivity by expanding the equations in the inverse of the number of spacetime dimensions D. We obtain an analytic expression for the critical temperature as a function of the conformal dimension of the condensate operator. Its accuracy for 3+1-dimensional superconductors is better than 15%. The analysis reveals a simple, and quantitative, explanation for the onset of the superconducting instability, as well as universal features of holographic superconductivity in the large D limit. In particular, this allows to easily compute the effects of backreaction on the critical temperature.

hep-th↗

arXiv2013

Holographic collisions in confining theories

We study the gravitational dual of a high-energy collision in a confining gauge theory. We consider a linearized approach in which two point particles traveling in an AdS-soliton background suddenly collide to form an object at rest (presumably a black hole for large enough center-of-mass energies). The resulting radiation exhibits the features expected in a theory with a mass gap: late-time power law tails of the form t^(-3/2), the failure of Huygens' principle and distortion of the wave pattern as it propagates. The energy spectrum is exponentially suppressed for frequencies smaller than the gauge theory mass gap. Consequently, we observe no memory effect in the gravitational waveforms. At larger frequencies the spectrum has an upward-stairway structure, which corresponds to the excitation of the tower of massive states in the confining gauge theory. We discuss the importance of phenomenological cutoffs to regularize the divergent spectrum, and the aspects of the full non-linear collision that are expected to be captured by our approach.

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