High frequency quasi-normal modes for black holes with generic singularities II: Asymptotically non-flat spacetimes

The possibility that the asymptotic quasi-normal mode (QNM) frequencies can be used to obtain the Bekenstein-Hawking entropy for the Schwarzschild black hole -- commonly referred to as Hod's conjecture -- has received considerable attention. To test this conjecture, using monodromy technique, attempts have been made to analytically compute the asymptotic frequencies for a large class of black hole spacetimes. In an earlier work, two of the current authors computed the high frequency QNMs for scalar perturbations of $(D+2)$ dimensional spherically symmetric, asymptotically flat, single horizon spacetimes with generic power-law singularities. In this work, we extend these results to asymptotically non-flat spacetimes. Unlike the earlier analyses, we treat asymptotically flat and de Sitter spacetimes in a unified manner, while the asymptotic anti-de Sitter spacetimes is considered separately. We obtain master equations for the asymptotic QNM frequency for all the three cases. We show that for all the three cases, the real part of the asymptotic QNM frequency -- in general -- is not proportional to ln(3) thus indicating that the Hod's conjecture may be restrictive.Comment: 16 pages; 3 Figures; Revtex4; Final Version -- To appear in CQ

Estimating parameters of binary black holes from gravitational-wave observations of their inspiral, merger and ringdown

We characterize the expected statistical errors with which the parameters of black-hole binaries can be measured from gravitational-wave (GW) observations of their inspiral, merger and ringdown by a network of second-generation ground-based GW observatories. We simulate a population of black-hole binaries with uniform distribution of component masses in the interval $(3,80)~M_\odot$, distributed uniformly in comoving volume, with isotropic orientations. From signals producing signal-to-noise ratio $\geq 5$ in at least two detectors, we estimate the posterior distributions of the binary parameters using the Bayesian parameter estimation code LALInference. The GW signals will be redshifted due to the cosmological expansion and we measure only the "redshifted" masses. By assuming a cosmology, it is possible to estimate the gravitational masses by inferring the redshift from the measured posterior of the luminosity distance. We find that the measurement of the gravitational masses will be in general dominated by the error in measuring the luminosity distance. In spite of this, the component masses of more than $50\%$ of the population can be measured with accuracy better than $\sim 25\%$ using the Advanced LIGO-Virgo network. Additionally, the mass of the final black hole can be measured with median accuracy $\sim 18\%$. Spin of the final black hole can be measured with median accuracy $\sim 5\% ~(17\%)$ for binaries with non-spinning (aligned-spin) black holes. Additional detectors in Japan and India significantly improve the accuracy of sky localization, and moderately improve the estimation of luminosity distance, and hence, that of all mass parameters. We discuss the implication of these results on the observational evidence of intermediate-mass black holes and the estimation of cosmological parameters using GW observations.Comment: 9 pages, 5 figure

TIME-DEPENDENT SYSTEMS AND CHAOS IN STRING THEORY

One of the phenomenal results emerging from string theory is the AdS/CFT correspondence or gauge-gravity duality: In certain cases a theory of gravity is equivalent to a dual gauge theory, very similar to the one describing non-gravitational interactions of fundamental subatomic particles. A difficult problem on one side can be mapped to a simpler and solvable problem on the other side using this correspondence. Thus one of the theories can be understood better using the other. The mapping between theories of gravity and gauge theories has led to new approaches to building models of particle physics from string theory. One of the important features to model is the phenomenon of confinement present in strong interaction of particle physics. This feature is not present in the gauge theory arising in the simplest of the examples of the duality. However this N = 4 supersymmetric Yang-Mills gauge theory enjoys the property of being integrable, i.e. it can be exactly solved in terms of conserved charges. It is expected that if a more realistic theory turns out to be integrable, solvability of the theory would lead to simple analytical expressions for quantities like masses of the hadrons in the theory. In this thesis we show that the existing models of confinement are all nonintegrable--such simple analytic expressions cannot be obtained. We moreover show that these nonintegrable systems also exhibit features of chaotic dynamical systems, namely, sensitivity to initial conditions and a typical route of transition to chaos. We proceed to study the quantum mechanics of these systems and check whether their properties match those of chaotic quantum systems. Interestingly, the distribution of the spacing of meson excitations measured in the laboratory have been found to match with level-spacing distribution of typical quantum chaotic systems. We find agreement of this distribution with models of confining strong interactions, conforming these as viable models of particle physics arising from string theory

Integrability Lost

It is known that classical string dynamics in pure AdS_5\times S^5 is integrable and plays an important role in solvability. This is a deep and central issue in holography. Here we investigate similar classical integrability for a more realistic confining background and provide a negative answer. The dynamics of a class of simple string configurations in AdS soliton background can be mapped to the dynamics of a set of non-linearly coupled oscillators. In a suitable limit of small fluctuations we discuss a quasi-periodic analytic solution of the system. However numerics indicates chaotic behavior as the fluctuations are not small. Integrability implies the existence of a regular foliation of the phase space by invariant manifolds. Our numerics shows how this nice foliation structure is eventually lost due to chaotic motion. We also verify a positive Lyapunov index for chaotic orbits. Our dynamics is roughly similar to other known non-integrable coupled oscillators systems like Henon-Heiles equations.Comment: Acknowledged grant

Confining Backgrounds and Quantum Chaos in Holography

Classical world-sheet string theory has recently been shown to be nonintegrable and chaotic in various confining string theory backgrounds -- the AdS soliton background in particular. In this paper we study a minisuperspace quantization of the theory and look at properties of the spectrum like the distribution of level spacing, which are indicative of quantum order or chaos. In the quantum spectrum we find a gradual transition from chaotic (Wigner GOE) to integrable (Poisson) regime as we look at higher energies. This is expected since our system is integrable asymptotically, and at higher energies, the dynamics is entirely dominated by the kinetic terms.Comment: 10 pages, 5 figures; v2: References adde

Dissipative nonlinear dynamics in holography

We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behavior very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behavior, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of the operator dual to the scalar field. Our setup can also be used to study quenchlike behavior in strongly coupled nonlinear systems

On Dumb Holes and their Gravity Duals

Inhomogeneous fluid flows which become supersonic are known to produce acoustic analogs of ergoregions and horizons. This leads to Hawking-like radiation of phonons with a temperature essentially given by the gradient of the velocity at the horizon. We find such acoustic dumb holes in charged conformal fluids and use the fluid-gravity correspondence to construct dual gravity solutions. A class of quasinormal modes around these gravitational backgrounds perceive a horizon. Upon quantization, this implies a thermal spectrum for these modes.Comment: 24 pages, 4 figure

Physical Time-Varying Transfer Functions as Generic Low-Overhead Power-SCA Countermeasure

Mathematically-secure cryptographic algorithms leak significant side channel information through their power supplies when implemented on a physical platform. These side channel leakages can be exploited by an attacker to extract the secret key of an embedded device. The existing state-of-the-art countermeasures mainly focus on the power balancing, gate-level masking, or signal-to-noise (SNR) reduction using noise injection and signature attenuation, all of which suffer either from the limitations of high power/area overheads, performance degradation or are not synthesizable. In this article, we propose a generic low-overhead digital-friendly power SCA countermeasure utilizing physical Time-Varying Transfer Functions (TVTF) by randomly shuffling distributed switched capacitors to significantly obfuscate the traces in the time domain. System-level simulation results of the TVTF-AES implemented in TSMC 65nm CMOS technology show > 4000x MTD improvement over the unprotected implementation with nearly 1.25x power and 1.2x area overheads, and without any performance degradation