Analogue simulations of quantum gravity with fluids
Samuel L. Braunstein, Mir Faizal, Lawrence M. Krauss, Francesco Marino, Naveed A. Shah
备注：
Accepted version in Nature Reviews Physics. A view-only version of the manuscript with edited figures and additional references can be accessed at the link https://rdcu.be/dj6CN
The recent technological advances in controlling and manipulating fluids have enabled the experimental realization of acoustic analogues of gravitational black holes. A flowing fluid provides an effective curved spacetime on which sound waves can propagate, allowing the simulation of gravitational geometries and related phenomena. The last decade has witnessed a variety of hydrodynamic experiments testing disparate aspects of black hole physics culminating in the recent experimental evidence of Hawking radiation and Penrose superradiance. In this Perspective, we discuss the potential use of analogue hydrodynamic systems beyond classical general relativity towards the exploration of quantum gravitational effects. These include possible insights into the information-loss paradox, black hole physics with Planck-scale quantum corrections, emergent gravity scenarios and the regularization of curvature singularities. We aim at bridging the gap between the non-overlapping communities of experimentalists working with classical and quantum fluids and quantum-gravity theorists, illustrating the opportunities made possible by the latest experimental and theoretical developments in these important areas of research
We investigate the possibility to generate quantum-correlated quasi-particles utilizing analogue gravity systems. The quantumness of these correlations is a key aspect of analogue gravity effects and their presence allows for a clear separation between classical and quantum analogue gravity effects. However, experiments in analogue systems, such as Bose-Einstein condensates, and shallow water waves, are always conducted at non-ideal conditions, in particular, one is dealing with dispersive media at nonzero temperatures. We analyze the influence of the initial temperature on the entanglement ge…
It is shown that when a strong electric field is turned on as a background in a charged scalar field, the vacuum state of the scalar field becomes exponentially amplified. This is an analogue to gravity induced vacuum amplification, where the vacuum state becomes exponentially amplified for some geometries.
We consider dissipation of surface waves on fluids, with a view to its effects on analogue gravity experiments. We begin by reviewing some general properties of wave dissipation, before restricting our attention to surface waves and the dissipative role played by viscosity there. Finally, with particular focus on water, we consider several experimental setups inspired by analogue gravity: the analogue Hawking effect, the black hole laser, the analogue wormhole, and double bouncing at the wormhole entrance. Dissipative effects are considered in each, and we give estimates for their optimized ex…
This chapter gives an introduction to the connection between the physics of water waves and analogue gravity. Only a basic knowledge of fluid mechanics is assumed as a prerequisite.
We conjecture an extension of the fluid/gravity correspondence to the null pressureless fluid case via gravitational shockwave solutions, and use it to propose an embedding of the fluid Hopfion in gravity. A nonlinear gravitational "helicity" is also proposed, analogous with the helicity of electromagnetism and fluid dynamics.
The expansion of hadronic matter that takes place immediately after a heavy ion collision has certain similarity with the cosmological expansion. We study the analogue geometry of the expanding hadronic fluid, using the the formalism of relativistic acoustic geometry. We show that the propagation of massless pions provides a geometric analog of expanding spacetime equivalent to an open (k=-1)FRW cosmology. Here, we study general conditions for the formation of a trapped region with the inner boundary as a marginally trapped surface.
We show that Schwarzschild black hole solutions in asymptotically Anti-de Sitter (AdS) and de Sitter (dS) spaces may, up to a conformal factor, be reproduced in the framework of analogue gravity. The aforementioned derivation is performed using relativistic and non-relativistic Bose-Einstein condensates. In addition, we demonstrate that the (2+1) planar AdS black hole can be mapped into the non-relativistic acoustic metric. Given that AdS black holes are extensively employed in the gauge/gravity duality, we then comment on the possibility to study the AdS/CFT correspondence and gravity/fluid d…
Empirical confirmation in some areas of physics is obscure; for example in Hawking radiation. However, the analogue gravity can simulate these phenomena in condensed matter systems. That is an important question whether the observation of these phenomena in the condensed matter systems can be confirmatory of the original phenomenon or not. In this work we answer affirmatively to this question via structuralism.
The dynamics of sound in a fluid is intrinsically nonlinear. We derive the consequences of this fact for the analogue gravitational field experienced by sound waves, by first describing generally how the nonlinearity of the equation for phase fluctuations back-reacts onto the definition of the background providing the effective space-time metric. Subsequently, we use the the analytical tool of Riemann invariants in one-dimensional motion to derive source terms of the effective gravitational field stemming from nonlinearity. Finally, we show that the consequences of nonlinearity we derive can b…
The problem of finding a minimal-time path for an aeroplane travelling in a wind flow has a simple formulation in terms of analogue gravity. This paper gives an elementary explanation with equations and some numerical solutions.
The quasiparticle content of a quantum field depends on the observer, in particular on its motional state, on the way the observer's detector couples to the quantum field, and on the frequency standard in which the detector carried by the observer measures the quanta to be detected. I review a procedure of making this fundamental property of quantum field theory experimentally manifest using quantum-optical means in Bose-Einstein condensates.
Formal analogies between the ordinary differential equations describing geophysical flows and Friedmann cosmology are developed. As a result, one obtains Lagrangian and Hamiltonian formulations of these equations, while laboratory experiments aimed at testing geophysical flows are shown to constitute analogue gravity systems for cosmology.
We describe how analogues of a Hawking evaporating black hole as well as the Unruh effect for an oscillatory, accelerating photodetector in vacuum may be realized using superconducting, microwave circuits that are fashioned out of Josephson tunnel junction and film bulk acoustic resonator elements.
We set up a tunneling approach to the analogue Hawking effect in the case of models of analogue gravity which are affected by dispersive effects. An effective Schroedinger-like equation for the basic scattering phenomenon IN->P+N*, where IN is the incident mode, P is the positive norm reflected mode, and N* is the negative norm one, signalling particle creation, is derived, aimed to an approximate description of the phenomenon. Horizons and barrier penetration play manifestly a key-role in giving rise to pair-creation. The non-dispersive limit is also correctly recovered. Drawbacks of the mode…
The quantization of gravity coupled to a perfect fluid model leads to a Schrödinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic equation of state $p = αρ$; solutions can also be found for the radiative non-flat case. The wave packets are constructed, from which the expectation value for the scale factor is determined. The quantum scenarios reveal a bouncing Universe, free from singularity. We show that such quantum cosmological perfect fluid models admit a universal classical analogue, repre…
We introduce an analogue model for a nonglobally hyperbolic spacetime in terms of a two-dimensional fluid. This is done by considering the propagation of sound waves in a radial flow with constant velocity. We show that the equation of motion satisfied by sound waves is the wave equation on $AdS_2\times S^1$. Since this spacetime is not globally hyperbolic, the dynamics of the Klein-Gordon field is not well defined until boundary conditions at the spatial boundary of $AdS_2$ are prescribed. On the analogue model end, those extra boundary conditions provide an effective description of the point…
Analogue gravity is based on a mathematical identity between quantum field theory in curved space-time and the propagation of perturbations in certain condensed matter systems. But not every curved space-time can be simulated in such a way, because one does not only need a condensed matter system that generates the desired metric tensor, but that system then also has to obey its own equations of motion. And specifying the metric tensor that one wishes to realize usually overdetermines the underlying condensed matter system, such that its equations of motion are in general not fulfilled, in whi…
We review the fluid/gravity correspondence which relates the dynamics of Einstein's equations (with negative cosmological constant) to the dynamics of relativistic Navier-Stokes equations.
Taking the principles of quantum mechanics as they stand and applying them to gravity, leads to the conclusion that one might be able to generate superpositions of spacetimes, at least formally. We analyze such a possibility from an analogue gravity perspective. We present an analogue toy model consisting of a Bose-Einstein condensate in a double-well potential and identify the states that could potentially be interpreted as superposition of effective spacetimes. These states are unstable and the source of instability from a microscopic point of view can be related to the absence of a well-def…
Analogue gravity systems offer many insights into gravitational phenomena, both at the classical and at the semiclassical level. The existence of an underlying Minkowskian structure (or Galilean in the non-relativistic limit) in the laboratory has been argued to directly forbid the simulation of geometries with Closed Timelike Curves (CTCs) within analogue systems. We will show that this is not strictly the case. In principle, it is possible to simulate spacetimes with CTCs whenever this does not entail the presence of a chronological horizon separating regions with CTCs from regions that do n…
This article is an introduction for a theme issue following a Scientific Discussion Meeting on \emph{The next generation of analogue gravity experiments} held at the Royal Society in December 2019. This theme issue comprises a collection of recent advances of the research programme, as well as their philosophical implications, that were presented at the meeting.
In this paper we provide fully covariant proofs of some theorems on shear-free perfect fluids. In particular, we explicitly show that any shear-free perfect fluid with the acceleration proportional to the vorticity vector (including the simpler case of vanishing acceleration) must be either non-expanding or non-rotating. We also show that these results are not necessarily true in the Newtonian case, and present an explicit comparison of shear-free dust in Newtonian and relativistic theories in order to see where and why the differences appear.
We show that non-linear dynamics of a scalar field ϕ may be described as a mod- ification of the spacetime geometry. Thus, the self-interaction is interpreted as a coupling of the scalar field with an effective gravitational metric that is constructed with ϕ itself. We prove that this process is universal, that is, it is valid for arbi- trary Lagrangian. Our results are compared to usual analogue models of gravitation, where the emergence of a metric appears as a consequence of linear perturbation.
A family of spherically symmetric solutions with horizon in the model with m-component anisotropic fluid is presented. The metrics are defined on a manifold that contains a product of n-1 Ricci-flat "internal" spaces. The equation of state for any s-th component is defined by a vector U^s belonging to R^{n + 1}. The solutions are governed by moduli functions H_s obeying non-linear differential equations with certain boundary conditions imposed. A simulation of black brane solutions in the model with antisymmetric forms is considered. An example of solution imitating M_2-M_5 configuration (in D…
A nonlinear scalar field theory from which an effective metric can be deduced is considered. This metric is shown to be compatible with requirements of general relativity. It is demonstrated that there is a class of solutions which fulfill both the nonlinear field equation as the Einstein equations for this metric.
We discuss recent developments in the hydrodynamic description of strongly coupled conformal field theories using the AdS/CFT correspondence. In particular, we review aspects of the fluid-gravity correspondence which provides a map between a class of inhomogeneous, dynamical, black hole solutions in asymptotically AdS spacetimes and arbitrary fluid flows in the strongly interacting boundary field theory. We explain how the geometric duals to the fluid dynamics are constructed in a boundary derivative expansion and use the construction to extract the hydrodynamic transport coefficients. In addi…
Analogue gravity is based on the simple observation that perturbations propagating in several physical systems can be described by a quantum field theory in a curved spacetime. While phenomena like Hawking radiation are hardly detectable in astrophysical black holes, these effects may be experimentally tested in analogue systems. In this Thesis, focusing on Bose-Einstein condensates, we present our recent results about analogue models of gravity from three main perspectives: as laboratory tests of quantum field theory in curved spacetime, for the techniques that they provide to address various…
Simulation and experimental realization of acoustic black holes in analogue gravity systems have lead to a novel understanding of relevant phenomena such as Hawking radiation or superradiance. We explore here the possibility to use relativistic systems for simulating rotating black hole solutions and possibly get an acoustic analogue of a Kerr black hole. In doing so we demonstrate a precise relation between non-relativistic and relativistic solutions and provide a new class of vortex solutions for relativistic systems. Such solutions might be used in the future as a test bed in numerical simu…
Based on the previous paper arXiv:1207.5309, we investigate the possibility to find out the bulk viscosity of dual fluid at the finite cutoff surface via gravity/fluid correspondence in Einstein-Maxwell gravity. We find that if we adopt new conditions to fix the undetermined parameters contained in the stress tensor and charged current of the dual fluid, two new terms appear in the stress tensor of the dual fluid. One new term is related to the bulk viscosity term, while the other can be related to the perturbation of energy density. In addition, since the parameters contained in the charged c…
We address the issues related to the presence of the quantum potential term in a BEC on the observable Analogue Gravity systems. We show that the quantum potential term apparently gives rise to massive scalar excitations of length scales of the order $\mathcal{O}(1/ξ)$ in the lower dimensional space. Since, in 'analogue models', there is a window for experimental observations generally in (2 + 1) or even lower dimensional space, one has to take proper account of the presence of these massive excitations to interpret the results.
Using the formalism of relativistic acoustic geometry we study the expanding chiral fluid in the regime of broken chiral symmetry near the QCD chiral phase transition temperature T_c. The dynamics of pions below T_c is described by the equation of motion for a massless scalar field propagating in curved spacetime similar to an open FRW universe. The metric tensor depends locally on the soft pion dispersion relation and the four-velocity of the fluid. In the neighborhood of the critical point an analogue trapped region forms with the analogue trapped horizon as its boundary. We show that the as…
Exact results concerning ray-tracing methods in Plebanski-Tamm media are derived. In particular, Hamilton equations describing the propagation of quasi-plane wave electromagnetic fields in the geometrical optics regime are explicitly written down in terms of the 3-metric representing the properties of the optical analogue, anisotropic medium. We exemplify our results by obtaining the trajectories of light in the resulting analogue medium recreating Gödel's universe.
General Relativity's Kerr metric is famous for its many symmetries which are responsible for the separability of the Hamilton-Jacobi equation governing the geodesic motion and of the Teukolsky equation for wave dynamics. We show that there is a unique stationary and axisymmetric Newtonian gravitational potential that has exactly the same dual property of separable point-particle and wave motion equations. This `Kerr metric analogue' of Newtonian gravity is none other than Euler's 18th century problem of two-fixed gravitating centers.
Analogue gravity can be used to reproduce the phenomenology of quantum field theory in curved spacetime and in particular phenomena such as cosmological particle creation and Hawking radiation. In black hole physics, taking into account the backreaction of such effects on the metric requires an extension to semiclassical gravity and leads to an apparent inconsistency in the theory: the black hole evaporation induces a breakdown of the unitary quantum evolution leading to the so called information loss problem. Here we show that analogue gravity can provide an interesting perspective on the res…
In the context of field theory in curved spacetimes, it is known that suitable background spacetime geometries can trigger instabilities of fields, leading to exponential growth of their (quantum and classical) fluctuations --- a phenomenon called $\textit{vacuum awakening}$ in the quantum context, which in some classical scenarios seeds $\textit{spontaneous scalarization/vectorization}$. Despite its conceptual interest, an actual observation in nature of this effect is uncertain since it depends on the existence of fields with appropriate masses and couplings in strong-gravity regimes. Here, …
Ultrashort laser pulse filaments in dispersive nonlinear Kerr media induce a moving refractive index perturbation which modifies the space-time geometry as seen by co-propagating light rays. We study the analogue geometry induced by the filament and show that one of the most evident features of filamentation, namely conical emission, may be precisely reconstructed from the geodesics. We highlight the existence of favorable conditions for the study of analogue black hole kinematics and Hawking type radiation.
Quantum fluctuations on curved spacetimes cause the emission of pairs of particles from the quantum vacuum, as in the Hawking effect from black holes. We use an optical analogue to gravity to investigate the influence of the curvature on quantum emission. Due to dispersion, the spacetime curvature varies with frequency here. We analytically calculate for all frequencies the particle flux, correlations and entanglement. We find that horizons increase the flux with a characteristic spectral shape. The photon number correlations transition from multi- to two-mode, with close to maximal entangleme…
We discuss the backreaction force exerted by quantum fluctuations in dilute Bose-Einstein condensates onto the motion of the classical background, derived by an ab initio approach from microscopic physics. It is shown that the effective-action method, widely employed in semiclassical quantum gravity, fails to give the full backreaction force. The failure of the effective-action method is traced back, inter alia, to the problem of the correct choice of the fundamental variables and the related operator ordering issues.
Quantum effects of fields on curved spacetimes may be studied in the laboratory thanks to quantum fluids. Here we use a polariton fluid to study the Hawking effect, the correlated emission from the quantum vacuum at the acoustic horizon. We show how out-of-equilibrium physics affects the dispersion relation, and hence the emission and propagation of correlated waves: the fluid properties on either side of the horizon are critical to observing the Hawking effect. We find that emission may be optimised by supporting the phase and density of the fluid upstream of the horizon in a regime of optica…
We consider a moving refractive index perturbation in an optical medium as an optical analogue to waves under the influence of gravity. We describe the dielectric medium by the Lagrangian of the Hopfield model. We supplement the field theory in curved spacetime for this model to solve the scattering problem for all modes and frequencies analytically. Because of dispersion, the kinematic scenario of the field modes may contain optical event horizons for some frequencies. We calculate the spectra of spontaneous emission in the frame co-moving with the perturbation and in the laboratory frame. We…
Why are "analogue spacetimes'' interesting? For the purposes of this workshop the answer is simple: Analogue spacetimes provide one with physically well-defined and physically well-understood concrete models of many of the phenomena that seem to be part of the yet incomplete theory of "quantum gravity'', or more accessibly, "quantum gravity phenomenology''. Indeed "analogue spacetimes'' provide one with concrete models of "emergence'' (whereby the effective low-energy theory can be radically different from the high-energy microphysics). They also provide many concrete and controlled models of …
As the long wavelength limit of the AdS/CFT correspondence, the gravity/fluid correspondence has been shown to be a useful tool for extracting properties of the fluid on the boundary dual to the gravity in the bulk. In this paper, after briefly reviewing the algorithm of gravity/fluid correspondence, we discuss the results of its application on bulk gravity with a $U(1)$ gauge field. In the presence of a $U(1)$ gauge field, the dual fluid possesses more interesting properties such as its charge current. Furthermore, an external field $A_μ^{ext}$ could affect the charge current, and the $U(1)$ …
An analogue model for the $\text{AdS}_2$ spacetime has been recently introduced by Mosna, Pitelli and Richartz [Phys. Rev. D 94, 104065 (2016)] by considering sound waves propagating on a fluid with an ill-defined velocity profile at its source/sink. The wave propagation is then uniquely defined only when one imposes an extra boundary condition at the source/sink (which corresponds to the spatial infinity of $\text{AdS}_2$). Here we show that, once this velocity profile is smoothed out at the source/sink, the need for extra boundary conditions disappears. This, in turn, corresponds to deformat…
So called "analogue models" use condensed matter systems (typically hydrodynamic) to set up an "effective metric" and to model curved-space quantum field theory in a physical system where all the microscopic degrees of freedom are well understood. Known analogue models typically lead to massless minimally coupled scalar fields. We present an extended "analogue space-time" programme by investigating a condensed-matter system - in and beyond the hydrodynamic limit - that is in principle capable of simulating the massive Klein-Gordon equation in curved spacetime. Since many elementary particles h…
The vorticity statistics characterises both the direct and the inverse turbulent cascades of two-dimensional fluid flows. The fluid/gravity correspondence relates fluid flows to black brane dynamics. We construct the holographic vorticity for relativistic and non-relativistic fluids in terms of the gravitational black brane data, and relate it to the horizon vorticity expressed as a Weyl scalar. We discuss the statistical scaling structure of the horizon geometry.
We discuss a class of teleparallel scalar-torsion theories of gravity, which is parametrized by five free functions of the scalar field. The theories are formulated covariantly using a flat, but non-vanishing spin connection. We show how the actions of different theories within this class are related via conformal transformations of the tetrad and redefinitions of the scalar field, and derive the corresponding transformation laws for the free function in the action. From these we construct a number of quantities which are invariant under these transformations, and use them to write the action …
This talk gives an overview of the recently-formulated Fluid/Gravity correspondence, which was developed in the context of gauge/gravity duality. Mathematically, it posits that Einstein's equations (with negative cosmological constant) in d+1 dimensions capture the (generalized) Navier-Stokes equations in d dimensions. Given an arbitrary fluid dynamical solution, we can systematically construct a corresponding asymptotically AdS black hole spacetime with a regular horizon whose properties mimic that of the fluid flow. Apart from an overview of this construction, we describe some of its applica…
Freelance Fluid/Gravity Correspondence, 3d Analysis
School of Physics, Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）；Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院）
It was predicted that the spin precession frequency of a stationary gyroscope shows various anomalies in the strong gravity regime if its orbit shrinks, and eventually its precession frequency becomes arbitrarily high very close to the horizon of a rotating black hole. Considering the gravity waves of a flowing fluid with vortex in a shallow basin, that acts as a rotating analogue black hole, one can observe the predicted strong gravity effect on the spin precession in the laboratory. Attaching a thread with the buoyant particles and anchored it to the bottom of the fluid container with a shor…
