Analogue Black Hole Research Articles

Slow sound in a duct, effective transonic flows, and analog black holes

We propose a new system suitable for studying analogue gravity effects, consisting of a gas flowing in a duct with a compliant wall. Effective transonic flows are obtained from uniform, low Mach number flows through the reduction of the one-dimensional speed of sound induced by the wall compliance. We show that the modified equation for linear perturbations can be written in a Hamiltonian form. We perform a one-dimensional reduction consistent with the canonical formulation, and deduce the analogue metric along with the first dispersive term. In a weak dispersive regime, the spectrum emitted from a sonic horizon is numerically shown to be Planckian, and with a temperature fixed by the analogue surface gravity.

Recent progress on analog gravity and related issues

Of the four kinds of fundamental interactions in nature, gravity is the first known to humankind, but at the same time, it seems to be the least understood. A self-consistent theory of quantum gravity is still elusive. Even though, the efforts to unify quantum theory and general relativity continue, and recent researches show that analog gravitational systems open up new possibilities for our understanding of the nature of gravity. The analog gravity provides us concrete non-gravitational physical systems to study the quantum effects in curved spacetime such as the Hawking radiation both theoretically and experimentally on the one hand, while on the other hand, the techniques dealing with issues in curved spacetime can also be applied to the analog systems themselves and shed light on them in return. In this paper, we review various analog models that capture different aspects of the behaviors of gravitational systems. First, we introduce the analog of the bending of light in curved spacetime with artificial metamaterials based on transformation optics, which is an analog of a classical general relativistic effect. We then review Unruhs sonic black hole model. When the speed of the background fluid is faster than the speed of sound in the fluid, one creates a sonic analog of a gravitational black hole. If the flow of an ideal fluid is irrotational, then the equation of motion describing the acoustic disturbance is identical to the dAlembertian equation of a minimally coupled massless scalar filed in a curved spacetime, which forms the foundation of the phonon Hawking radiation in analog systems. Unruhs sonic black hole model has become a paradigm for experimental verification of quantum effects in curved spacetime, and there have been, in recent years, many attempts to realize it in analogue systems such as the Bose-Einstein condensate, ion traps, optical fibers, and etc. Other related issues, such as the detection of modified vacuum fluctuations, which are intrinsically related to quantum effects in curved space, by means of superconducting circuit devices, and the metamaterial models of cosmological evolutions are also reviewed. Finally, we give an outlook for the future research.

Stationary bound states of massless scalar fields around black holes and black hole analogues

We discuss stationary bound states, a.k.a. clouds, for a massless test scalar field around Kerr black holes (BHs) and spinning acoustic BH analogues. In view of the absence of a mass term, the trapping is achieved via enclosing the BH — scalar field system in a cavity and imposing Dirichlet or Neumann boundary conditions. We discuss the variation of these bounds states with the discrete parameters that label them, as well as their spatial distribution, complementing results in our previous work [C. L. Benone, L. C. B. Crispino, C. Herdeiro and E. Radu, Phys. Rev. D91 (2015) 104038].

Measuring the entanglement of analogue Hawking radiation by the density-density correlation function

We theoretically study the entanglement of Hawking radiation pairs emitted by an analogue black hole. We find that this entanglement can be measured by the experimentally accessible density-density correlation function, vastly simplifying the measurement. We find that while the Hawking radiation exiting the black hole might be Planck-distributed, the correlations between the Hawking radiation and the partner particles has a distribution which is weaker but broader than Planckian. Thus, the high energy tail of the distribution of Hawking radiation should be entangled, whereas the low energy part should not be. This confirms a previous numerical study. The full Peres-Horodecki criterion is considered, as well as a simpler criterion in the stationary, homogeneous case. Our method applies to systems which are sufficiently cold that the thermal phonons can be neglected.

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.

Quasinormal acoustic oscillations in the Michel flow

We study spherical and nonspherical linear acoustic perturbations of the Michel flow, which describes the steady radial accretion of a perfect fluid into a nonrotating black hole. The dynamics of such perturbations are governed by a scalar wave equation on an effective curved background geometry determined by the acoustic metric, which is constructed from the spacetime metric and the particle density and four-velocity of the fluid. For the problem under consideration in this article the acoustic metric has the same qualitative features as an asymptotically flat, static and spherically symmetric black hole, and thus it represents a natural astrophysical analogue black hole. As for the case of a scalar field propagating on a Schwarzschild background, we show that acoustic perturbations of the Michel flow exhibit quasi-normal oscillations. Based on a new numerical method for determining the solutions of the radial mode equation, we compute the associated frequencies and analyze their dependency on the radii of the event and sonic horizons and the angular momentum number. Our results for the fundamental frequencies are compared to those obtained from an independent numerical Cauchy evolution, finding good agreement between the two approaches. When the radius of the sonic horizon is large compared to the event horizon radius, we find that the quasi-normal frequencies scale approximately like the surface gravity associated with the sonic horizon.

Nonlinear effects in time-dependent transonic flows: An analysis of analog black hole stability

We study solutions of the one-dimensional Gross-Pitaevskii equation to better understand dynamical instabilities occurring in flowing atomic condensates. Whereas transonic stationary flows can be fully described in simple terms, time-dependent flows exhibit a wide variety of behaviors. When the sound speed is crossed once, we observe that flows analogous to black holes obey something similar to the so-called no hair theorem since their late time profile is stationary and uniquely fixed by parameters entering the Hamiltonian and conserved quantities. For flows analogous to white holes, at late time one finds a macroscopic undulation in the supersonic side which has either a fixed amplitude, or a widely varying one signaling a quasi periodic emission of solitons on the subsonic side. When considering flows which cross the sound speed twice, we observe various scenarios which can be understood from the above behaviors, and from the hierarchy of the growth rates of the dynamical instabilities characterizing such flows.

High overtone quasinormal modes of analog black holes and the small scale structure of the background fluid

The goal of this paper is to build a foundation for, and explore the possibility of, using high overtone quasinormal modes (QNMs) of analog black holes to probe the small scale (microscopic) structure of a background fluid in which an analog black hole is formed. This may provide a tool to study the small scale structure of some interesting quantum systems such as Bose–Einstein condensates (BECs). In order to build this foundation, we first look into the hydrodynamic case where we calculate the high overtone QNM frequencies of a 3+1 dimensional canonical non-rotating acoustic black hole. The leading order calculations have been done earlier in the literature. Here, we obtain the first order correction. We then analyze the high overtone QNMs of acoustic black holes in a BEC using the linearized Gross–Pitaevskii equation. We point out that at the high overtone QNM limit, the only term that is important in the linearized Gross–Pitaevskii equation is the quantum potential term, which is a small scale effect.

Nonstationary analogue black holes

We study the existence of analogue nonstationary spherically symmetric black holes. The prime example is the acoustic model see Unruh (1981 Phys. Rev. Lett. 46 1351). We consider also a more general class of metrics that could be useful in other physical models of analogue black and white holes. We give examples of the appearance of black holes and of disappearance of white holes. We also discuss the relation between the apparent and the event horizons for the case of analogue black holes. In the end we study the inverse problem of determination of black or white holes by boundary measurements for the spherically symmetric nonstationary metrics.

Bose-Einstein condensates with derivative and long-range interactions as set-ups for analog black holes

General types of Bose-Einstein condensates are considered. The formation of black-hole analogues is examined for both short- and long-range interactions for arbitrary spatial dimensions greater than 2. The former case includes nonlinear derivative terms plus an inevitable external potential, while the latter one consists solely of gravitylike self-interactions for which intrinsic formation of analogue Schwarzschild-type background space-times is possible. The corresponding geometries are studied, and it is shown how they can be made stable. Their Hawking temperature is estimated, and it is found that in certain setups it can be significantly increased, thus providing better detectability.

Observation of self-amplifying Hawking radiation in an analogue black-hole laser

It has been proposed that a black hole horizon should generate Hawking radiation. In order to test this theory, we have created a narrow, low density, very low temperature atomic Bose-Einstein condensate, containing an analog black hole horizon and an inner horizon, as in a charged black hole. We observe Hawking radiation emitted by the black hole. This is the output of the black hole laser. We also observe the exponential growth of a standing wave between the horizons. The latter results from interference between the negative energy partners of the Hawking radiation and the negative energy particles reflected from the inner horizon. We thus observe self-amplifying Hawking radiation.

Black Hole Analogue in Bose–Einstein Condensation

We have proposed a black hole analogue in a Bose–Einstein condensation. By introducing the Painleve co-ordinates and using K–G equations, we have obtained the critical temperature of the black hole analogue in a Bose–Einstein condensation.

Quantum entanglement in analogue Hawking radiation: When is the final state nonseparable?

We study the quantum entanglement of the quasiparticle pairs emitted by analogue black holes. We use a phenomenological description of the spectra in dispersive media to study the domains in parameter space where the final state is non-separable. In stationary flows, three modes are involved in each sector of fixed frequency, and not two as in homogeneous situations. The third spectator mode acts as an environment for the pairs, and the strength of the coupling significantly reduces the quantum coherence. The non-separability of the pairs emitted by white holes are also considered, and compared with that of black holes.

Two-point function for a BEC analogue black hole when a mass term is present

Two-point function for a BEC analogue black hole when a mass term is present

3D flat holography: entropy and logarithmic corrections

We compute the leading corrections to the Bekenstein-Hawking entropy of the Flat Space Cosmological (FSC) solutions in 3D flat spacetimes, which are the flat analogues of the BTZ black holes in AdS3. The analysis is done by a computation of density of states in the dual 2D Galilean Conformal Field Theory and the answer obtained by this matches with the limiting value of the expected result for the BTZ inner horizon entropy as well as what is expected for a generic thermodynamic system. Along the way, we also develop other aspects of holography of 3D flat spacetimes.

Hawking radiation with dispersion versus breakdown of the WKB approximation

Inspired by the condensed matter analogues of black holes (a.k.a. dumb holes), we study Hawking radiation in the presence of a modified dispersion relation which becomes super-luminal at large wave-numbers. In the usual stationary coordinates $(t,x)$, one can describe the asymptotic evolution of the wave-packets in WKB, but this WKB approximation breaks down in the vicinity of the horizon, thereby allowing for a mixing between initial and final creation and annihilation operators. Thus, one might be tempted to identify this point where WKB breaks down with the moment of particle creation. However, using different coordinates $(\tau,U)$, we find that one can evolve the waves so that WKB in these coordinates is valid throughout this transition region -- which contradicts the above identification of the breakdown of WKB as the cause of the radiation. Instead, our analysis suggests that the tearing apart of the waves into two different asymptotic regions (inside and outside the horizon) is the major ingredient of Hawking radiation.

Table‐top cosmology with Bose‐Einstein condensates

Cosmic inflation is the theory that the universe underwent a violent, rapid expansion at the beginning of time, giving rise to much of the observed structure in the universe 1. This theory is supported by indirect observational evidence from many different sources (e.g. see 2). However, direct experimental investigation of inflation is of course impossible. For this reason there has been considerable interest in analog models for astrophysics (e.g. see 3), in which analogous behavior is studied in systems that are experimentally convenient. Due to their cleanness and great flexibility, dilute ultra-cold atomic gases (particularly Bose-Einstein condensates) form an attractive system for realizing such analog models. Indeed, a number of such table-top-astrophysics experiments have been conducted with Bose-Einstein condensates. For example, supernova-like collapse and explosion dynamics 4, controlled by modifying inter-atomic interactions using Feshbach resonances, and later interpreted as cosmological particle creation 5; Faster-than-sound flow of a condensate has been used to produce a sonic black hole analog 6; The in situ measurements of density fluctuations in a quenched quasi-two-dimensional condensate have demonstrated Sakharov like oscillations, analogous to the process thought to give rise to the anisotropy in the cosmic microwave background radiation 7. In Quantum simulations of the early universe Opanchuk and collaborators 8 propose using a two component condensate to simulate the inflationary phase of the early universe (see Fig. 1). In appropriate limits the relative phase between the two fields describing the condensate components is known to obey the sine-Gordon equation 9. The sine-Gordon model (SGM) is one of many scalar models for inflation that have been investigated in cosmology. It is thought to provide an acceptable model of the beginning of inflation where, starting from an unstable vacuum state, quantum fluctuations seed the cosmological inhomogeneities that lead to structure formation. However, the SGM likely fails to describe the end of inflation as its scalar potential does not generate efficient parametric resonances needed to ensure reheating of the universe 10, 11. The SGM also has applications in cosmology beyond inflation, and is a model for the “axion” matter field considered as a promising candidate for dark matter12. An important innovation in the scheme proposed by Opanchuk et al. is the introduction of a microwave (linear) coupling between the components that provides a practical way to initialize the system into an unstable vacuum state and controllably explore the subsequent evolution. Approximate numerical simulations, performed using the truncated Wigner approach, verify dynamical clustering can occur within experimentally realistic parameter regimes. The main challenge to realizing the proposed scenario will be finding an atom, and a pair of internal states, with suitable interaction parameters. It is likely that such an atom will be available given the increasing diversity of atomic species that have been Bose-condensed, and the great control over interactions afforded by Feshbach resonances. Aided by the rich toolbox of techniques available to ultra-cold atomic physics an array of opportunities present themselves for developing this line of research, such as: Engineering gravitational-like effects through including long range interactions, e.g. through electromagnetically induced gravity 13; Enhancing quantum fluctuations through stronger interactions or by confining the system in an optical lattice; Engineering richer models by including more spin states and other species of atoms.

Analog of gravitational force in hyperbolic metamaterials

Subwavelength confinement of light in nonlinear hyperbolic metamaterials due to formation of spatial solitons has attracted much recent attention because of its seemingly counterintuitive behavior. In order to achieve self-focusing in a hyperbolic wire medium, a nonlinear self-defocusing Kerr medium must be used as a dielectric host. Here we demonstrate that this behavior finds a natural explanation in terms of the analog of gravity. A wave equation describing the propagation of extraordinary light inside hyperbolic metamaterials exhibits (2+1)-dimensional Lorentz symmetry. The role of time in the corresponding effective three-dimensional Minkowski space-time is played by the spatial coordinate aligned with the optical axis of the metamaterial. Nonlinear optical Kerr effect ``bends'' this space-time resulting in effective gravitational force between extraordinary photons. In order for the effective gravitational constant to be positive, a negative self-defocusing Kerr medium must be used as a host. If gravitational self-interaction is strong enough, the spatial soliton may collapse into a black hole analog.

Scattering by a draining bathtub vortex

We present an analysis of scattering by a fluid-mechanical ``black hole analogue,'' known as the draining bathtub vortex: a two-dimensional flow that possesses both a sonic horizon and an ergoregion. We consider the scattering of a plane wave of fixed frequency impinging upon the vortex. At low frequency, we encounter a modified Aharonov-Bohm effect. At high frequencies, we observe regular ``orbiting'' oscillations in the scattering length, due to interference between contra-orbiting rays. We present approximate formulas for both effects and a selection of numerical results obtained by summing partial-wave series. Finally, we examine interference patterns in the vicinity of the vortex and highlight the prospects for experimental investigation.

Quantum vacuum emission in a nonlinear optical medium illuminated by a strong laser pulse

A strong light pulse propagating in a nonlinear Kerr medium produces a change in the refractive index, which makes light travel at different speeds inside and outside the pulse. By tuning the pulse velocity, an analog black hole horizon can be obtained in a suitable frequency window. In this paper, we develop a quantum theory of light propagation for this system, including the frequency dispersion of the refractive index of the medium by coupling the electromagnetic field to matter polarization fields. In a configuration with a single black hole horizon, the spectrum of spontaneously emitted particles presents some similarities with Hawking radiation. Furthermore, even in horizonless systems spontaneous vacuum emission is still possible due to the dispersive nature of the medium, yet with dramatically different spectral properties.