Topics in gravitational-wave science : macroscopic quantum mechanics and black hole physics

The theories of relativity and quantum mechanics, the two most important physics discoveries of the 20th century, not only revolutionized our understanding of the nature of space-time and the way matter exists and interacts, but also became the building blocks of what we currently know as modern physics. My thesis studies both subjects in great depths --- this intersection takes place in gravitational-wave physics.

Gravitational waves are "ripples of space-time", long predicted by general relativity. Although indirect evidence of gravitational waves has been discovered from observations of binary pulsars, direct detection of these waves is still actively being pursued. An international array of laser interferometer gravitational-wave detectors has been constructed in the past decade, and a first generation of these detectors has taken several years of data without a discovery. At this moment, these detectors are being upgraded into second-generation configurations, which will have ten times better sensitivity. Kilogram-scale test masses of these detectors, highly isolated from the environment, are probed continuously by photons. The sensitivity of such a quantum measurement can often be limited by the Heisenberg Uncertainty Principle, and during such a measurement, the test masses can be viewed as evolving through a sequence of nearly pure quantum states.

The first part of this thesis (Chapter 2) concerns how to minimize the adverse effect of thermal fluctuations on the sensitivity of advanced gravitational detectors, thereby making them closer to being quantum-limited. My colleagues and I present a detailed analysis of coating thermal noise in advanced gravitational-wave detectors, which is the dominant noise source of Advanced LIGO in the middle of the detection frequency band. We identified the two elastic loss angles, clarified the different components of the coating Brownian noise, and obtained their cross spectral densities.

The second part of this thesis (Chapters 3-7) concerns formulating experimental concepts and analyzing experimental results that demonstrate the quantum mechanical behavior of macroscopic objects - as well as developing theoretical tools for analyzing quantum measurement processes. In Chapter 3, we study the open quantum dynamics of optomechanical experiments in which a single photon strongly influences the quantum state of a mechanical object. We also explain how to engineer the mechanical oscillator's quantum state by modifying the single photon's wave function.

In Chapters 4-5, we build theoretical tools for analyzing the so-called "non-Markovian" quantum measurement processes. Chapter 4 establishes a mathematical formalism that describes the evolution of a quantum system (the plant), which is coupled to a non-Markovian bath (i.e., one with a memory) while at the same time being under continuous quantum measurement (by the probe field). This aims at providing a general framework for analyzing a large class of non-Markovian measurement processes. Chapter 5 develops a way of characterizing the non-Markovianity of a bath (i.e.,whether and to what extent the bath remembers information about the plant) by perturbing the plant and watching for changes in the its subsequent evolution. Chapter 6 re-analyzes a recent measurement of a mechanical oscillator's zero-point fluctuations, revealing nontrivial correlation between the measurement device's sensing noise and the quantum rack-action noise.

Chapter 7 describes a model in which gravity is classical and matter motions are quantized, elaborating how the quantum motions of matter are affected by the fact that gravity is classical. It offers an experimentally plausible way to test this model (hence the nature of gravity) by measuring the center-of-mass motion of a macroscopic object.

The most promising gravitational waves for direct detection are those emitted from highly energetic astrophysical processes, sometimes involving black holes - a type of object predicted by general relativity whose properties depend highly on the strong-field regime of the theory. Although black holes have been inferred to exist at centers of galaxies and in certain so-called X-ray binary objects, detecting gravitational waves emitted by systems containing black holes will offer a much more direct way of observing black holes, providing unprecedented details of space-time geometry in the black-holes' strong-field region.

The third part of this thesis (Chapters 8-11) studies black-hole physics in connection with gravitational-wave detection.

Chapter 8 applies black hole perturbation theory to model the dynamics of a light compact object orbiting around a massive central Schwarzschild black hole. In this chapter, we present a Hamiltonian formalism in which the low-mass object and the metric perturbations of the background spacetime are jointly evolved. Chapter 9 uses WKB techniques to analyze oscillation modes (quasi-normal modes or QNMs) of spinning black holes. We obtain analytical approximations to the spectrum of the weakly-damped QNMs, with relative error O(1/L^2), and connect these frequencies to geometrical features of spherical photon orbits in Kerr spacetime. Chapter 11 focuses mainly on near-extremal Kerr black holes, we discuss a bifurcation in their QNM spectra for certain ranges of (l,m) (the angular quantum numbers) as a/M → 1. With tools prepared in Chapter 9 and 10, in Chapter 11 we obtain an analytical approximate for the scalar Green function in Kerr spacetime.

Can the viscosity in astrophysical black hole accretion disks be close to its string theory bound?

String theory and gauge/gravity duality suggest the lower bound of shear viscosity (eta) to entropy density (s) for any matter to be mu h/4 pi k(B), when h and k(B) are reduced Planck and Boltzmann constants respectively and mu <= 1. Motivated by this, we explore eta/s in black hole accretion flows, in order to understand if such exotic flows could be a natural site for the lowest eta/s. Accretion flow plays an important role in black hole physics in identifying the existence of the underlying black hole. This is a rotating shear flow with insignificant molecular viscosity, which could however have a significant turbulent viscosity, generating transport, heat and hence entropy in the flow. However, in presence of strong magnetic field, magnetic stresses can help in transporting matter independent of viscosity, via celebrated Blandford-Payne mechanism. In such cases, energy and then entropy produces via Ohmic dissipation. In,addition, certain optically thin, hot, accretion flows, of temperature greater than or similar to 10(9) K, may be favourable for nuclear burning which could generate/absorb huge energy, much higher than that in a star. We find that eta/s in accretion flows appears to be close to the lower bound suggested by theory, if they are embedded by strong magnetic field or producing nuclear energy, when the source of energy is not viscous effects. A lower bound on eta/s also leads to an upper bound on the Reynolds number of the flow.

The possibility of primordial black hole direct detection

This thesis explores the possibility of directly detecting blackbody emission from Primordial Black Holes (PBHs). A PBH might form when a cosmological density uctuation with wavenumber k, that was once stretched to scales much larger than the Hubble radius during ination, reenters inside the Hubble radius at some later epoch. By modeling these uctuations with a running{tilt power{law spectrum (n(k) = n0 + a1(k)n1 + a2(k)n2 + a3(k)n3; n0 = 0:951; n1 = ????0:055; n2 and n3 unknown) each pair (n2,n3) gives a di erent n(k) curve with a maximum value (n+) located at some instant (t+). The (n+,t+) parameter space [(1:20,10????23 s) to (2:00,109 s)] has t+ = 10????23 s{109 s and n+ = 1:20{2:00 in order to encompass the formation of PBHs in the mass range 1015 g{1010M (from the ones exploding at present to the most massive known). It was evenly sampled: n+ every 0.02; t+ every order of magnitude. We thus have 41 33 = 1353 di erent cases. However, 820 of these ( 61%) are excluded (because they would provide a PBH population large enough to close the Universe) and we are left with 533 cases for further study. Although only sub{stellar PBHs ( 1M ) are hot enough to be detected at large distances we studied PBHs with 1015 g{1010M and determined how many might have formed and still exist in the Universe. Thus, for each of the 533 (n+,t+) pairs we determined the fraction of the Universe going into PBHs at each epoch ( ), the PBH density parameter (PBH), the PBH number density (nPBH), the total number of PBHs in the Universe (N), and the distance to the nearest one (d). As a rst result, 14% of these (72 cases) give, at least, one PBH within the observable Universe, one{third being sub{stellar and the remaining evenly spliting into stellar, intermediate mass and supermassive. Secondly, we found that the nearest stellar mass PBH might be at 32 pc, while the nearest intermediate mass and supermassive PBHs might be 100 and 1000 times farther, respectively. Finally, for 6% of the cases (four in 72) we might have substellar mass PBHs within 1 pc. One of these cases implies a population of 105 PBHs, with a mass of 1018 g(similar to Halley's comet), within the Oort cloud, which means that the nearest PBH might be as close as 103 AU. Such a PBH could be directly detected with a probability of 10????21 (cf. 10????32 for low{energy neutrinos). We speculate in this possibility.

Quantum gravity effects in rotating black hole spacetimes

The aim of this work is to explore, within the framework of the presumably asymptotically safe Quantum Einstein Gravity, quantum corrections to black hole spacetimes, in particular in the case of rotating black holes. We have analysed this problem by exploiting the scale dependent Newton s constant implied by the renormalization group equation for the effective average action, and introducing an appropriate "cutoff identification" which relates the renormalization scale to the geometry of the spacetime manifold. We used these two ingredients in order to "renormalization group improve" the classical Kerr metric that describes the spacetime generated by a rotating black hole. We have focused our investigation on four basic subjects of black hole physics. The main results related to these topics can be summarized as follows. Concerning the critical surfaces, i.e. horizons and static limit surfaces, the improvement leads to a smooth deformation of the classical critical surfaces. Their number remains unchanged. In relation to the Penrose process for energy extraction from black holes, we have found that there exists a non-trivial correlation between regions of negative energy states in the phase space of rotating test particles and configurations of critical surfaces of the black hole. As for the vacuum energy-momentum tensor and the energy conditions we have shown that no model with "normal" matter, in the sense of matter fulfilling the usual energy conditions, can simulate the quantum fluctuations described by the improved Kerr spacetime that we have derived. Finally, in the context of black hole thermodynamics, we have performed calculations of the mass and angular momentum of the improved Kerr black hole, applying the standard Komar integrals. The results reflect the antiscreening character of the quantum fluctuations of the gravitational field. Furthermore we calculated approximations to the entropy and the temperature of the improved Kerr black hole to leading order in the angular momentum. More generally we have proven that the temperature can no longer be proportional to the surface gravity if an entropy-like state function is to exist.

A Calogero formulation for four-dimensional black-hole microstates

We extract the leading-order entropy of a four-dimensional extremal black hole in N=2N=2 ungauged supergravity by formulating the CFT1 that is holographically dual to its near-horizon AdS2 geometry, in terms of a rational Calogero model with a known counting formula for the degeneracy of states in its Hilbert space.

Cassini states for black hole binaries

Cassini states correspond to the equilibria of the spin axis of a body when its orbit is perturbed. They were initially described for planetary satellites, but the spin axes of black hole binaries also present this kind of equilibria. In previous works, Cassini states were reported as spin-orbit resonances, but actually the spin of black hole binaries is in circulation and there is no resonant motion. Here we provide a general description of the spin dynamics of black hole binary systems based on a Hamiltonian formalism. In absence of dissipation, the problem is integrable and it is easy to identify all possible trajectories for the spin for a given value of the total angular momentum. As the system collapses due to radiation reaction, the Cassini states are shifted to different positions, which modifies the dynamics around them. This is why the final spin distribution may differ from the initial one. Our method provides a simple way of predicting the distribution of the spin of black hole binaries at the end of the inspiral phase.

Higher-Order Nonlinearity In Accretion Disks: Quasi-Periodic Oscillations Of Black Hole And Neutron Star Sources And Their Spin

We propose a unified model to explain Quasi-Periodic Oscillation (QPO), particularly of high frequency, observed from black hole and neutron star systems globally. We consider accreting systems to be damped harmonic oscillators exhibiting epicyclic oscillations with higher-order nonlinear resonance to explain QPO. The resonance is expected to be driven by the disturbance from the compact object at its spin frequency. The model explains various properties parallelly for both types of the compact object. It describes QPOs successfully for ten different compact sources. Based on this, we predict the spin frequency of the neutron star Sco X-1 and specific angular momentum of black holes GRO J1655–40, XTE J1550–564, H1743–322, and GRS 1915+105.

Massive black-hole binary inspirals: results from the LISA parameter estimation taskforce

The LISA Parameter Estimation Taskforce was formed in September 2007 to provide the LISA Project with vetted codes, source distribution models and results related to parameter estimation. The Taskforce's goal is to be able to quickly calculate the impact of any mission design changes on LISA's science capabilities, based on reasonable estimates of the distribution of astrophysical sources in the universe. This paper describes our Taskforce's work on massive black-hole binaries (MBHBs). Given present uncertainties in the formation history of MBHBs, we adopt four different population models, based on (i) whether the initial black-hole seeds are small or large and (ii) whether accretion is efficient or inefficient at spinning up the holes. We compare four largely independent codes for calculating LISA's parameter-estimation capabilities. All codes are based on the Fisher-matrix approximation, but in the past they used somewhat different signal models, source parametrizations and noise curves. We show that once these differences are removed, the four codes give results in extremely close agreement with each other. Using a code that includes both spin precession and higher harmonics in the gravitational-wave signal, we carry out Monte Carlo simulations and determine the number of events that can be detected and accurately localized in our four population models.

Search for chaos in neutron star systems: Is Cyg X-3 a black hole?

The accretion disk around a compact object is a nonlinear general relativistic system involving magnetohydrodynamics. Naturally, the question arises whether such a system is chaotic (deterministic) or stochastic (random) which might be related to the associated transport properties whose origin is still not confirmed. Earlier, the black hole system GRS 1915+105 was shown to be low-dimensional chaos in certain temporal classes. However, so far such nonlinear phenomena have not been studied fairly well for neutron stars which are unique for their magnetosphere and kHz quasi-periodic oscillation (QPO). On the other hand, it was argued that the QPO is a result of nonlinear magnetohydrodynamic effects in accretion disks. If a neutron star exhibits chaotic signature, then what is the chaotic/correlation dimension? We analyze RXTE/PCA data of neutron stars Sco X-1 and Cyg X-2, along with the black hole Cyg X-1 and the unknown source Cyg X-3, and show that while Sco X-1 and Cyg X-2 are low dimensional chaotic systems, Cyg X-1 and Cyg X-3 are stochastic sources. Based on our analysis, we argue that Cyg X-3 may be a black hole.

The mixed black hole partition function for the STU model

We evaluate the mixed partition function for dyonic BPS black holes using the recently proposed degeneracy formula for the STU model. The result factorizes into the OSV mixed partition function times a proportionality factor. The latter is in agreement with the measure factor that was recently conjectured for a class of N = 2 black holes that contains the STU model.

Spectral states and accretion geometries in Galactic black hole binaries

Black hole X-ray binaries, binary systems where matter from a companion star is accreted by a stellar mass black hole, thereby releasing enormous amounts of gravitational energy converted into radiation, are seen as strong X-ray sources in the sky. As a black hole can only be detected via its interaction with its surroundings, these binary systems provide important evidence for the existence of black holes. There are now at least twenty cases where the measured mass of the X-ray emitting compact object in a binary exceeds the upper limit for a neutron star, thus inferring the presence of a black hole. These binary systems serve as excellent laboratories not only to study the physics of accretion but also to test predictions of general relativity in strongly curved space time. An understanding of the accretion flow onto these, the most compact objects in our Universe, is therefore of great importance to physics. We are only now slowly beginning to understand the spectra and variability observed in these X-ray sources. During the last decade, a framework has developed that provides an interpretation of the spectral evolution as a function of changes in the physics and geometry of the accretion flow driven by a variable accretion rate. This doctoral thesis presents studies of two black hole binary systems, Cygnus~X-1 and GRS~1915+105, plus the possible black hole candidate Cygnus~X-3, and the results from an attempt to interpret their observed properties within this emerging framework. The main result presented in this thesis is an interpretation of the spectral variability in the enigmatic source Cygnus~X-3, including the nature and accretion geometry of its so-called hard spectral state. The results suggest that the compact object in this source, which has not been uniquely identified as a black hole on the basis of standard mass measurements, is most probably a massive, ~30 Msun, black hole, and thus the most massive black hole observed in a binary in our Galaxy so far. In addition, results concerning a possible observation of limit-cycle variability in the microquasar GRS~1915+105 are presented as well as evidence of `mini-hysteresis' in the extreme hard state of Cygnus X-1.

Upper mass limit for neutron star stability against black hole formation

Starting from the exact general relativistic expression for the total energy of selfgravitating spherically distributed matter and using the minimum energy priciple, we calculate the upper mass limit for a neutron star to be 3.1 solar masses.

Classical integrability in the BTZ black hole

Using the fact the BTZ black hole is a quotient of AdS(3) we show that classical string propagation in the BTZ background is integrable. We construct the flat connection and its monodromy matrix which generates the non-local charges. From examining the general behaviour of the eigen values of the monodromy matrix we determine the set of integral equations which constrain them. These equations imply that each classical solution is characterized by a density function in the complex plane. For classical solutions which correspond to geodesics and winding strings we solve for the eigen values of the monodromy matrix explicitly and show that geodesics correspond to zero density in the complex plane. We solve the integral equations for BMN and magnon like solutions and obtain their dispersion relation. We show that the set of integral equations which constrain the eigen values of the monodromy matrix can be identified with the continuum limit of the Bethe equations of a twisted SL(2, R) spin chain at one loop. The Landau-Lifshitz equations from the spin chain can also be identified with the sigma model equations of motion.

Implications of a viscosity bound on black hole accretion

Motivated by the viscosity bound in gauge/gravity duality, we consider the ratio of shear viscosity (eta) to entropy density (s) in black hole accretion flows. We use both an ideal gas equation of state and the QCD equation of state obtained from lattice for the fluid accreting onto a Kerr black hole. The QCD equation of state is considered since the temperature of accreting matter is expected to approach 10(12) K in certain hot flows. We find that in both the cases eta/s is small only for primordial black holes and several orders of magnitude larger than any known fluid for stellar and supermassive black holes. We show that a lower bound on the mass of primordial black holes leads to a lower bound on eta/s and vice versa. Finally we speculate that the Shakura-Sunyaev viscosity parameter should decrease with increasing density and/or temperatures. (C) 2012 Elsevier B.V. All rights reserved.