We construct algebras of diff-invariant observables in a global de Sitter universe with two observers and a free scalar QFT in two dimensions. We work in the strict $G_N \rightarrow 0$ limit, but allow the observers to have an order one mass in cosmic units. The observers are fully quantized. In the limit when the observers have infinite mass and are localized along geodesics at the North and South poles, it was shown in previous work \cite{CLPW} that their algebras are mutually commuting type II$_1$ factors. Away from this limit, we show that the algebras fail to commute and that they are type I non-factors. Physically, this is because the observers' trajectories are uncertain and state-dependent, and they may come into causal contact. We compute out-of-time-ordered correlators along an observer's worldline, and observe a Lyapunov exponent given by $\frac{4 π}{β_{\text{dS}}}$, as a result of observer recoil and de Sitter expansion. This should be contrasted with results from AdS gravity, and exceeds the chaos bound associated with the de Sitter temperature by a factor of two. We also discuss how the cosmological horizon emerges in the large mass limit and comment on implications for de Sitter holography.
It is known that certain types of particle motion near black hole horizons are chaotic while it has been proposed the existence of a universal bound for their Lyapunov exponent. We discuss the relation between chaos and inaffinity in presence of black hole and cosmological horizons. We argue that although a relation between the Lyapunov exponent and the generalized surface gravity appears naturally, in general there is no reason for the Lyapunov exponent of classical trajectories to be bounded in generic spacetimes with horizon. Moreover, we show that the de Sitter spacetime and cosmological h…
To find the origin of chaos near black hole horizon in string-theoretic AdS/CFT correspondence, we perform a chaos analysis of a suspended string in AdS black hole backgrounds. It has a definite CFT interpretation: chaos of Wilson loops, or in other words, sensitive time-evolution of a quark antiquark force in thermal gauge theories. Our nonlinear numerical simulation of the suspended Nambu-Goto string shows chaos, which would be absent in pure AdS background. The calculated Lyapunov exponent $λ$ satisfies the universal bound $λ\leq 2πT_{\rm H}$ for the Hawking temperature $T_{\rm H}$. We also…
In this paper, we have studied the variation of the chaos bound in two regions of the torus-like black hole, i.e., the region close to the black hole horizon and the region at a certain distance from the black hole horizon. The angular momentum of the particle affects the effective potential and influences the magnitude of the chaotic behavior of the particle. Therefore, the angular momentum of particle is important in the study. The angular momentum of a particle not only affects the particle equilibrium orbital position, but also affects the Lyapunov exponent. As the angular momentum of the …
Motion of a particle near a horizon of a spherically symmetric black hole is shown to possess a universal Lyapunov exponent of a chaos provided by its surface gravity. To probe the horizon, we introduce electromagnetic or scalar force to the particle so that it does not fall into the horizon. There appears an unstable maximum of the total potential where the evaluated maximal Lyapunov exponent is found to be independent of the external forces and the particle mass. The Lyapunov exponent is universally given by the surface gravity of the black hole. Unless there are other sources of a chaos, th…
The chaos bound in the near-horizon regions has been studied through the expansions of the metric functions on the horizon. In this paper, we investigate the chaos bound in the the near-horizon region and at a certain distance from the horizon of a charged Kiselev black hole. The value of the Lyapunov exponent is accurately calculated by a Jacobian matrix. The angular momentum of a charged particle around the black hole affects not only the exponent, but also the position of the equilibrium orbit. This position gradually moves away from the horizon with the increase of the angular momentum. We…
The information loss problem in black hole evaporation is one of fundamental issues. Its resolution requires more profound understanding of information storage mechanism in quantum systems. In this Letter, we argue that when multiple unknown parameters are stored in large entangled qudits, strong chaos generated by fast scrambling in high temperature limit yields an ordered information storage structure with decoupled quantum information capsules (QICs). A rotational isometry emerges in the quantum Fisher information metric. The isometry is expected to be observed in future experiments on cold…
Researches in the several decades have shown that the dynamics of gravity is closely related to thermodynamics of the horizon. In this paper, we derive the Friedmann acceleration equation based on the idea of "emergence of space" and thermodynamics of the Hubble horizon whose temperature is obtained from the unified first law of thermodynamics. Then we derive another evolution equation of the universe based on the energy balance relation $ρV_{H}=TS$. Combining the two evolution equations and the equation of state of the cosmic matter, we obtain the evolution solutions of the FRW universe. We f…
Cosmological brick walls & quantum chaotic dynamics of de Sitter horizons
Universidad de Oviedo（奥维耶多大学）；Instituto de Física Teórica UAM/CSIC（UAM/CSIC理论物理研究所）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Pohang University of Science and Technology（浦项科技大学）
We have proposed that the interior of a macroscopic Schwarzschild black hole (BH) consists of highly excited, long, closed, interacting strings and, as such, can be modeled as a collapsed polymer. It was previously shown that the scaling relations of the collapsed-polymer model agree with those of the BH. The current paper further substantiates this proposal with an investigation into some of its dynamical consequences. In particular, we show that the model predicts, without relying on gravitational effects, an emergent horizon. We further show that the horizon fluctuates quantum mechanically …
For a long time it is believed that black hole horizon are thermal and quantum mechanical in nature. The microscopic origin of this thermality is the main question behind our present investigation, which reveals possible importance of near horizon symmetry. It is this symmetry which is assumed to be spontaneously broken by the background spacetime, generates the associated Goldstone modes. In this paper we construct a suitable classical action for those Goldstone modes, and show that all the momentum modes experience nearly the same inverted harmonic potential, leading to an instability. Thank…
Horizon--orbit scale competition underlying chaos bound violation for spinning particles
School of Science, Xihua University（西华大学理学院）；Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所微重力实验室引力波实验中心）
It is possible to provide a physical interpretation for the field equations of gravity based on a thermodynamical perspective. The virtual degrees of freedom associated with the horizons perceived by the local Rindler observers, play a crucial role in this approach. In this context, the relation S=E/2T between the entropy (S), active gravitational mass (E) and temperature (T) - obtained previously in gr-qc/0308070 [CQG, 21, 4485 (2004)] - can be reinterpreted as the law of equipartition E = (1/2) nkT where n=A/L_P^2 is the number (density) of microscopic horizon degrees of freedom. Conversely,…
We show that holographic RG flow can be defined precisely such that it corresponds to emergence of spacetime. We consider the case of pure Einstein's gravity with a negative cosmological constant in the dual hydrodynamic regime. The holographic RG flow is a system of first order differential equations for radial evolution of the energy-momentum tensor and the variables which parametrize it's phenomenological form on hypersurfaces in a foliation. The RG flow can be constructed without explicit knowledge of the bulk metric provided the hypersurface foliation is of a special kind. The bulk metric…
It is suggested that many-body quantum chaos appears as the spontaneous symmetry breaking of unitarity in interacting quantum many-body systems. It has been shown that many-body level statistics, probed by the spectral form factor (SFF) defined as $K(η,t)=\langle|{\rm Tr}\, \exp(-ηH + itH)|^2\rangle$, is dominated by a diffuson-type mode in a field theory analysis. The key finding of this Letter is that the "unitary" $η=0$ case is different from the $η\to 0^{\pm}$ limit, with the latter leading to a finite mass of these modes due to interactions. This mass suppresses a rapid exponential ramp i…
Extreme-Mass-Ratio Inspirals Embedded in Dark Matter Halo: Existence of Homoclinic Orbit and Horizon-Induced Chaos
University of Science and Technology of China（中国科学技术大学）；CAS Key Laboratory for Researches in Galaxies and Cosmology, School of Astronomy and Space Science, University of Science and Technology of China（中国科学院星系与宇宙学重点实验室，中国科学技术大学天文与空间科学学院）；Shanghai University（上海大学）；Sogang University（西江大学）；Center for Quantum Spacetime, Sogang University（西江大学量子时空中心）
We calculate the thermal diffusivity $D = κ/c_ρ$ and butterfly velocity $v_B$ in holographic models that flow to AdS$_2 \times R^{d}$ fixed points in the infra-red. We show that both these quantities are governed by the same irrelevant deformation of AdS$_2$ and hence establish a simple relationship between them. When this deformation corresponds to a universal dilaton mode of dimension $Δ= 2$ then this relationship is always given by $D = v_B^2/(2 πT)$.
We investigate the "pole-skipping" phenomenon in holographic chaos. According to the pole-skipping, the energy-density Green's function is not unique at a special point in complex momentum plane. This arises because the bulk field equation has two regular near-horizon solutions at the special point. We study the regularity of two solutions more carefully using curvature invariants. In the upper-half $ω$-plane, one solution, which is normally interpreted as the outgoing mode, is in general singular at the future horizon and produces a curvature singularity. However, at the special point, both s…
We solve Einstein vacuum equations in a spacetime region up to the "center" of gravitational collapse. Within this region, we construct a sequence of marginally outer trapped surfaces (MOTS) with areas going to zero. These MOTS form a marginally outer trapped tube (apparent horizon). It emerges from a point and is smooth (except at that point) and spacelike. In the proof we employ a scale critical trapped surface formation criterion established by An and Luk and a new type of quasilinear elliptic equation is studied. The main conclusion of this paper proves a conjecture of Ashtekar on black ho…
Motivations for the existence of a fundamental preferred frame range from pure phenomenology to attempts to solve the non-renormalizability of quantum gravity, the problem of time (and scale), and the cosmological constant problem(s). In many explicit constructions, such as Einstein-Aether or Gravitational Aether theories, K-essence, Cuscuton theory, Shape Dynamics, or (non-projectable) Horava-Lifshitz gravity, the low energy theory contains a fluid (which defines a preferred frame) with superluminal or incompressible excitations. We study here the formation of black holes in the presence of s…
For a large enough Schwarzschild black hole, the horizon is a region of space where gravitational forces are weak; yet it is also a region leading to numerous puzzles connected to stringy physics. In this work, we analyze the process of gravitational collapse and black hole formation in the context of light-cone M theory. We find that, as a shell of matter contracts and is about to reveal a black hole horizon, it undergoes a thermodynamic phase transition. This involves the binding of D0 branes into D2's, and the new phase leads to large membranes of the size of the horizon. These in turn can …
We present an analytic microscopic theory showing that in a large class of spin-$\frac{1}{2}$ quasiperiodic quantum kicked rotors, a dynamical analog of the integer quantum Hall effect (IQHE) emerges from an intrinsic chaotic structure. Specifically, the inverse of the Planck's quantum ($h_e$) and the rotor's energy growth rate mimic the `filling fraction' and the `longitudinal conductivity' in conventional IQHE, respectively, and a hidden quantum number is found to mimic the `quantized Hall conductivity'. We show that for an infinite discrete set of critical values of $h_e$, the long-time ene…
We study the scattering of massless probes in the vicinity of the {\it photon-sphere} of asymptotically AdS black holes and horizon-free microstate geometries (fuzzballs). We find that these exhibit a chaotic behaviour characterised by exponentially large deviations of nearby trajectories. We compute the Lyapunov exponent $λ$ governing the exponential growth in $d$ dimensions and show that it is bounded from above by $λ_b = \sqrt{d{-}3}/2b_{\rm min}$ where $b_{\rm min}$ is the minimal impact parameter under which a massless particle is swallowed by the black hole or gets trapped in the fuzzbal…
National Tsing-Hua University（国立清华大学）；Center for Theory-Computation-Data Science Research, National Tsing-Hua University（国立清华大学理论计算数据科学研究中⼼）；National Center for Theoretical Sciences（国家理论科学中⼼）
Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting statistics of the local, total, and interaction energies. As in the spectral form factor, signatures of quantum chaos in the time domain dictate a dip-ramp-plateau structure in the characteristic function, i.e., the Fourier transform of the eigenvalue distribution. With this approach, we explore the fate of chaos in interacting subsystems that are locally maximally…
