Horizonless Geometries Research Articles

Tidal resonances for fuzzballs

We study the gravitational tidal response of D1D5, Top Star and (1,0,n) strata horizonless geometries. We find that the tidal interactions in fuzzball geometries, unlike in the case of black holes, exhibits a sequence of resonant peaks associated to the existence of metastable bound states. The spectrum of resonant frequencies is computed by semianalytical and numerical methods.

A microscopic model of black hole evaporation in two dimensions

We present a microscopic model of black hole (BH) ‘evaporation’ in asymptotically AdS2 spacetimes dual to the low energy sector of the SYK model. To describe evaporation, the SYK model is coupled to a bath comprising of Nf free scalar fields Φi. We consider a linear combination of couplings of the form OSY K(t)∑iΦi(0, t), where OSY K involves products of the Kourkoulou-Maldacena operator iJ/N{sum}_{k=1}^{N/2}{s}_k^{prime }{psi}_{2k-1}(t){psi}_{2k}(t) specified by a spin vector s′. We discuss the time evolution of a product of (i) a pure state of the SYK system, namely a BH microstate characterized by a spin vector s and an effective BH temperature TBH, and (ii) a Calabrese-Cardy state of the bath characterized by an effective temperature Tbath. We take Tbath ≪ TBH, and TBH much lower than the characteristic UV scale J of the SYK model, allowing a description in terms of the time reparameterization mode. Tracing over the bath degrees of freedom leads to a Feynman-Vernon type effective action for the SYK model, which we study in the low energy limit. The leading large N behaviour of the time reparameterization mode is found, as well as the Oleft(1/sqrt{N}right) fluctuations. The latter are characterized by a non-Markovian non-linear stochastic differential equation with non-local Gaussian noise. In a restricted range of couplings, we find two classes of solutions which asymptotically approach (a) a BH at a lower temperature, and (b) a horizonless geometry. We identify these with partial and complete BH evaporation, respectively. Importantly, the asymptotic solution in both cases involves the scalar product of the spin vectors s.s′, which carries some information about the initial state. By repeating the dynamical process O(N2) times with different choices of the spin vector s′, one can in principle reconstruct the initial BH microstate.

Hairy black holes in AdS with Robin boundary conditions

We study hairy black holes in Einstein-Maxwell-complex scalar theory in four-dimensional asymptotically global anti-de Sitter (AdS) spacetime when the Robin boundary conditions are imposed on the scalar field. This setup is dual to the double trace deformation of strongly interacting field theory on R × S2 by charged scalar operators. We identify the instability of the Reissner-Nordström-AdS (RNAdS) black holes under the Robin boundary conditions and construct backreacted geometries branching at the onset of the instability. Also considering associated horizonless geometries called boson stars, we obtain phase diagrams with fairly rich structure in the grand canonical ensemble depending on the boundary condition parameter or the deformation parameter, where phase transition occurs between thermal AdS, RNAdS, charged boson stars, and hairy black holes.

Non-BPS bubbling geometries in AdS3

We construct large classes of non-BPS smooth horizonless geometries that are asymptotic to AdS3 × S3 × T4 in type IIB supergravity. These geometries are supported by electromagnetic flux corresponding to D1-D5 charges. We show that Einstein equations for systems with eight commuting Killing vectors decompose into a set of Ernst equations, thereby admitting an integrable structure. This feature, which can a priori be applied to other {textrm{AdS}}_Dtimes mathcal{C} settings in supergravity, allows us to use solution-generating techniques associated with the Ernst formalism. We explicitly derive solutions by applying the charged Weyl formalism that we have previously developed. These are sourced internally by a chain of bolts that correspond to regions where the orbits of the commuting Killing vectors collapse smoothly. We show that these geometries can be interpreted as non-BPS T4 and S3 deformations on global AdS3 × S3 × T4 that are located at the center of AdS3. These non-BPS deformations can be made arbitrarily small and should therefore correspond to non-supersymmetric operators in the D1-D5 CFT. Finally, we also construct interesting bound states of non-extremal BTZ black holes connected by regular bolts.

Superstrata on orbifolded backgrounds

Some microstates of the Strominger-Vafa black hole are represented by smooth horizonless geometries called superstrata. The standard superstrata are deformations of AdS3 × S3, but there are also generalizations of superstrata on the orbifold (AdS3 × S3)/ℤp. In this paper, we discuss aspects of such orbifolded superstrata. We present a CFT perspective on the structure of orbifolded superstrata, showing that they can be constructed in a p-covering space of the orbifold CFT just as the standard superstrata. We also explicitly write down and study the geometry of the orbifolded superstrata, focusing on the difference from the non-orbifold case, p = 1. We discuss further generalization of superstrata to the ones on a fractional spectral flow of (AdS3 × S3)/ℤp. This generalization involves new fractional mode excitations of the CFT side. We estimate the number of those generalized superstrata, and show that their entropy is too small to account for the Strominger-Vafa entropy. We will discuss some implications of this result, related to the typical microstates of the black hole and the relevant supersymmetry index.

On the entropy of strings and branes

We show that the entropy of strings that wind around the Euclidean time circle is proportional to the Noether charge associated with translations along the T-dual time direction. We consider an effective target-space field theory which includes a large class of terms in the action with various modes, interactions and α′ corrections. The entropy and the Noether charge are shown to depend only on the values of fields at the boundary of space. The classical entropy, which is proportional to the inverse of Newton’s constant, is then calculated by evaluating the appropriate boundary term for various geometries with and without a horizon. We verify, in our framework, that for higher-curvature pure gravity theories, the Wald entropy of static neutral black hole solutions is equal to the entropy derived from the Gibbons-Hawking boundary term. We then proceed to discuss horizonless geometries which contain, due to the back-reaction of the strings and branes, a second boundary in addition to the asymptotic boundary. Near this “punctured” boundary, the time-time component of the metric and the derivatives of its logarithm approach zero. Assuming that there are such non-singular solutions, we identify the entropy of the strings and branes in this geometry with the entropy of the solution to all orders in α′. If the asymptotic region of an α′-corrected neutral black hole is connected through the bulk to a puncture, then the black hole entropy is equal to the entropy of the strings and branes. Later, we discuss configurations similar to the charged black p-brane solutions of Horowitz and Strominger, with the second boundary, and show that, to leading order in the α′ expansion, the classical entropy of the strings and branes is equal exactly to the Bekenstein-Hawking entropy. This result is extended to a configuration that asymptotes to AdS.

Turning rotating D-branes and black holes inside out their photon-halo

We extend our investigation on Couch-Torrence conformal inversions of black holes (BHs) and D-branes in various directions. We analyze asymptotically flat rotating charged BHs in $D=4$, in particular extremal rotating BHs in STU supergravity, and find invariance for special choices of the charges. Due to the dependence of the critical radii on the impact parameter(s), the relation between the scattering angle for geodesics outside the photon-halo and the inspiraling angle for geodesics inside the photon-halo is modified by the inclusion of a boundary term. We also consider rotating BHs in $D=5$ and rotating D3-branes and find invariance under generalized Couch-Torrence inversions for special choices of the angular momenta. Alas we don't find any similar symmetry for smooth horizonless geometries. Moreover, relying on the surprising connection between classical BH perturbation theory and quantum Seiberg-Witten curves for $\mathcal{N}=2$ SYM theories, we study scalar wave equations in these backgrounds and identify the near superradiant modes produced in near-extremal BH mergers. Finally, we study scalar fluctuations around Kerr-Newman BHs in ${\mathrm{AdS}}_{4}$ and find stringent conditions for generalized Couch-Torrence symmetry that are relaxed in the extremal case or by allowing a rescaling of the wave function.

Non-BPS floating branes and bubbling geometries

We derive a non-BPS linear ansatz using the charged Weyl formalism in string and M-theory backgrounds. Generic solutions are static and axially-symmetric with an arbitrary number of non-BPS sources corresponding to various brane, momentum and KKm charges. Regular sources are either four-charge non-extremal black holes or smooth non-BPS bubbles. We construct several families such as chains of non-extremal black holes or smooth non-BPS bubbling geometries and study their physics. The smooth horizonless geometries can have the same mass and charges as non-extremal black holes. Furthermore, we find examples that scale towards the four-charge BPS black hole when the non-BPS parameters are taken to be small, but the horizon is smoothly resolved by adding a small amount of non-extremality.

QNMs of branes, BHs and fuzzballs from quantum SW geometries

QNMs govern the linear response to perturbations of BHs, D-branes and fuzzballs and the gravitational wave signals in the ring-down phase of binary mergers. A remarkable connection between QNMs of neutral BHs in 4d and quantum SW geometries describing the dynamics of N=2 SYM theories has been recently put forward. We extend the gauge/gravity dictionary to a large class of gravity backgrounds including charged and rotating BHs of Einstein-Maxwell theory in d=4,5 dimensions, D3-branes, D1D5 ‘circular’ fuzzballs and smooth horizonless geometries; all related to N=2 SYM with a single SU(2) gauge group and fundamental matter. We find that photon-spheres, a common feature of all examples, are associated to degenerations of the classical elliptic SW geometry whereby a cycle pinches to zero size. Quantum effects resolve the singular geometry and lead to a spectrum of quantized energies, labelled by the overtone number n. We compute the spectrum of QNMs using exact WKB quantization, geodetic motion and numerical simulations and show excellent agreement between the three methods. We explicitly illustrate our findings for the case D3-brane QNMs.

Disformal mappings of spherical DHOST geometries

New solutions of DHOST theories can be generated by applying adisformal tranformation to a known seed solution. We examine the nature ofspherically symmetric solutions of DHOST gravity obtained by disformingstatic spherical scalar field solutions, or stealth solutions, of generalrelativity. It is shown that, in these cases, black hole horizons arenever created by disforming a black hole seed. New DHOST solutions arethen created by disforming two lesser known scalar field solutions ofgeneral relativity: Wyman's “other” solution and theHusain-Martinez-Nuñez one. These new solutions demonstrate that one canobtain black hole horizons, wormhole throats, or horizonless geometries bydisforming non-stealth, time-dependent, seeds.

Regular black holes in three dimensions

We find a plethora of new analytic black holes and globally regular horizonless spacetimes in three dimensions. The solutions involve a single real scalar field $\ensuremath{\phi}$ which always admits a magneticlike expression proportional to the angular coordinate. The new metrics, which satisfy ${g}_{tt}{g}_{rr}=\ensuremath{-}1$ and represent continuous generalizations of the Ba\~nados-Teitelboim-Zanelli (BTZ) one, solve the equations of Einstein gravity corrected by a new family of densities (controlled by unconstrained couplings) constructed from positive powers of $(\ensuremath{\partial}\ensuremath{\phi}{)}^{2}$ and certain linear combinations of ${R}^{ab}{\ensuremath{\partial}}_{a}\ensuremath{\phi}{\ensuremath{\partial}}_{b}\ensuremath{\phi}$ and $(\ensuremath{\partial}\ensuremath{\phi}{)}^{2}R$. Some of the solutions obtained describe black holes with one or several horizons. A set of them possesses curvature singularities, while others have conical or BTZ-like ones. Interestingly, in some cases the black holes have no singularity at all, being completely regular. Some of the latter are achieved without any kind of fine-tuning or constraint between the action parameters and/or the physical charges of the solution. An additional class of solutions describes globally regular and horizonless geometries.

Gravitational collapse in SYK models and Choptuik-like phenomenon

SYK model is a quantum mechanical model of fermions which is solvable at strong coupling and plays an important role as perhaps the simplest holographic model of quantum gravity and black holes. The present work considers a deformed SYK model and a sudden quantum quench in the deformation parameter. The system, as in the undeformed case, permits a low energy description in terms of pseudo Nambu Goldstone modes. The bulk dual of such a system represents a gravitational collapse, which is characterized by a bulk matter stress tensor whose value near the boundary shows a sudden jump at the time of the quench. The resulting gravitational collapse forms a black hole only if the deformation parameter ∆\U0001d716 exceeds a certain critical value ∆\U0001d716c and forms a horizonless geometry otherwise. In case a black hole does form, the resulting Hawking temperature is given by a fractional power Tbh∝ (∆\U0001d716 − ∆ \U0001d716c)1/2, which is reminiscent of the ‘Choptuik phenomenon’ of critical gravitational collapse.

Penrose process, superradiance, and ergoregion instabilities

Superradiant scattering is a radiation enhancement process that takes place in many contexts, and which has recently found exciting applications in astro and particle physics. In the framework of curved spacetime physics, it has been associated with the classical Penrose process for particles. Superradiance is usually also associated with bosonic fields around geometries with ergoregions and horizons. These notions are in clear tension however: the Penrose process occurs for horizonless geometries, and particles are composed of fermions. Here, we resolve the tension in its different aspects, by showing that (i) superradiance occurs for self-interacting fermions on flat spacetime; (ii) superradiance occurs also for horizonless geometries, where it leads to an ergoregion instability. Ultracompact, horizonless geometries will usually respond with echoes of growing amplitude, until rotational (or electrostatic) energy is extracted from the object; (iii) the Fourier-domain analysis leads to absence of superradiance when horizons are not present. We elucidate why this analysis fails to give meaningful results; (iv) finally, we show that superradiant, ergoregion instabilities have a particle analog of similar growth timescales and which can power the formation of a structure outside a compact, rotating star.

Parameter estimation of gravitational wave echoes from exotic compact objects

Relativistic ultracompact objects without an event horizon may be able to form in nature and merge as binary systems, mimicking the coalescence of ordinary black holes. The postmerger phase of such processes presents characteristic signatures, which appear as repeated pulses within the emitted gravitational waveform, i.e., echoes with variable amplitudes and frequencies. Future detections of these signals can shed new light on the existence of horizonless geometries, and provide new information on the nature of gravity in a genuine strong-field regime. In this work we analyze phenomenological templates used to characterize echolike structures produced by exotic compact objects, and we investigate for the first time the ability of current and future interferometers to constrain their parameters. Using different models with an increasing level of accuracy, we determine the features that can be measured with the largest precision, and we span the parameter space to find the most favorable configurations to be detected. Our analysis shows that current detectors may already be able to extract all the parameters of the echoes with good accuracy, and that multiple interferometers can measure frequencies and damping factors of the signals at the level of percent.

Smooth Horizonless Geometries Deep Inside the Black-Hole Regime.

We construct the first family of horizonless supergravity solutions that have the same mass, charges, and angular momenta as general supersymmetric rotating D1-D5-P black holes in five dimensions. This family includes solutions with arbitrarily small angular momenta, deep within the regime of quantum numbers and couplings for which a large classical black hole exists. These geometries are well approximated by the black-hole solution, and in particular exhibit the same near-horizon throat. Deep in this throat, the black-hole singularity is resolved into a smooth cap. We also identify the holographically dual states in the N=(4,4) D1-D5 orbifold conformal field theory (CFT). Our solutions are among the states counted by the CFT elliptic genus, and provide examples of smooth microstate geometries within the ensemble of supersymmetric black-hole microstates.

Black holes and wormholes subject to conformal mappings

Solutions of the field equations of theories of gravity which admit distinct conformal frame representations can look very different in these frames. We show that Brans class IV solutions describe wormholes in the Jordan frame (in a certain parameter range) but correspond to horizonless geometries in the Einstein frame. The reasons for such a change of behaviour under conformal mappings are elucidated in general, using Brans IV solutions as an example.

Black holes with a single Killing vector field: black resonators

We numerically construct asymptotically anti-de Sitter (AdS) black holes in four dimensions that contain only a single Killing vector field. These solutions, which we coin black resonators, link the superradiant instability of Kerr-AdS to the nonlinear weakly turbulent instability of AdS by connecting the onset of the superradiance instability to smooth, horizonless geometries called geons. Furthermore, they demonstrate non-uniqueness of Kerr-AdS by sharing asymptotic charges. Where black resonators coexist with Kerr-AdS, we find that the black resonators have higher entropy. Nevertheless, we show that black resonators are unstable and comment on the implications for the endpoint of the superradiant instability.

Structure of six-dimensional microstate geometries

We investigate the structure of smooth and horizonless microstate geometries in six dimensions, in the spirit of the five-dimensional analysis of Gibbons and Warner [arXiv:1305.0957]. In six dimensions, which is the natural setting for horizonless geometries with the charges of the D1-D5-P black hole, the natural black objects are strings and there are no Chern-Simons terms for the tensor gauge fields. However, we still find that the same reasoning applies: in absence of horizons, there can be no smooth stationary solutions without non-trivial topology. We use topological arguments to describe the Smarr formula in various examples: the uplift of the five-dimensional minimal supergravity microstates to six dimensions, the two-charge D1-D5 microstates, and the non-extremal JMaRT solution. We also discuss D1-D5-P superstrata and confirm that the Smarr formula gives the same result as for the D1-D5 supertubes which are topologically equivalent.

Role of angular momentum and cosmic censorship in(2+1)-dimensional rotating shell collapse

We study the gravitational collapse problem of rotating shells in three-dimensional Einstein gravity with and without a cosmological constant. Taking the exterior and interior metrics to be those of stationary metrics with asymptotically constant curvature, we solve the equations of motion for the shells from the Darmois-Israel junction conditions in the corotating frame. We study various collapse scenarios with arbitrary angular momentum for a variety of geometric configurations, including anti-de Sitter, de Sitter, and flat spaces. We find that the collapsing shells can form a BTZ black hole, a three-dimensional Kerr-dS spacetime, and an horizonless geometry of point masses under certain initial conditions. For pressureless dust shells, the curvature singularity is not formed due to the angular momentum barrier near the origin. However when the shell pressure is nonvanishing, we find that for all types of shells with polytropic-type equations of state (including the perfect fluid and the generalized Chaplygin gas), collapse to a naked singularity is possible under generic initial conditions. We conclude that in three dimensions angular momentum does not in general guard against violation of cosmic censorship.

Microstate Geometries and Entropy Enhancement

In string theory, black-hole backgrounds are far from unique and there are large families of completely smooth, horizonless geometries with the same structure as a black hole from infinity down to the neighborhood of the black-hole horizon. These microstate geometries cap off in foam of topological bubbles. I review some of the recent progress in constructing these smooth horizonless geometries and discuss some of the physical implications.