An Analytical and Numerical Treatment of Inclined Elliptical Orbits About a Kerr Black Hole

Since its publication in 1915, Einstein\u27s theory of general relativity has yielded significant results; they include: analytical solutions to the Einstein field equations; improved analysis of orbital dynamics; and the prediction of gravitational wave (GW) radiation. Gravitation is the weakest of the fundamental interactions; and theoretical models of GW generation and propagation show that its detection poses a significant technical challenge. Unlike the study of electromagnetic radiation, experiments within the laboratory are virtually impossible; so astronomical sources of GW, such as binary black hole systems, offer an alternative. But GW detection remains difficult. The matched filtering techniques used to discriminate a GW signal from background noise, require GW templates; thus a theoretical foreknowledge of binary black hole evolution is needed. Extreme mass-ratio binary black hole systems may be modelled by a massive Kerr black hole (KBH) and a test-particle in an inclined elliptical orbit. The GW spectrum is determined by the latus rectum (l), eccentricity (e), and inclination (iota) of the orbit, which gradually change with loss of energy and angular momentum. The evolution of these orbital characteristics is described by equations widely available in the literature; so it is essential that corroborative techniques be found to assure accuracy. The last stable orbit (LSO) is an important end-point at which the zoom and whirl of the test-particle becomes pronounced; this also affects the GW spectrum. An analytical and numerical study of the influence of KBH spin (S) on l and e of an equatorial LSO was performed first, followed by the derivation of a formula for the Carter constant (Q) of an inclined orbit in terms of S, l and e. This analysis drew attention to the abutment, a family of retrograde near-polar orbits, at which the consistency of evolution equations for Q with respect to those for l and e was tested. Further, the evolution of iota was also treated. To leading order in S, evolution equations for Q are consistent with those of l and e. The relationship between the evolution equation for iota with respect to l and e contains a second-order effect, which is yet to be fully characterised

Asteroseismology in Binary Stars with Applications of Bayesian Inference Tools

Space missions like Kepler have revolutionized asteroseismology, the science that infers the stellar interiors by studying oscillation frequency spectra of pulsating stars. Great advancements have been made in understanding solar-like oscillators. However, this is not the case for variable stars of intermediate masses, such asScutiand Doradus variables. By studying these stars in eclipsing binaries (EBs), model independent funda- mental parameters such as mass and radius can be inferred. On one hand, this synergy constrains the parameter space and facilitates the asteroseismic modeling, and this is shown for the Scuti type pulsating EB KIC 9851944. On the other hand, studies of binary stars must address the complexities such as mass transfer. KIC 8262223 is such an example, which consists of a mass-gaining Scuti primary and a pre-He white dwarf secondary. Some of the eccentric binary systems, the ‘heartbeat’ stars, show tidally excited oscillations. After briefly reviewing the linear theory of tidally forced stellar oscillations, we study the tidal pulsating binary KIC 3230227 and demonstrate that both amplitude and phase can be used to identify the tidally excited pulsation modes. We also discuss the variability of a Slowly Pulsating B-star KOI-81 and a Cataclysmic variable KIC 9406652. In the second part of this dissertation, we apply Bayesian statistics to some problems in binaries and asteroseismology with the help of packages BUGS and JAGS. Special attention is paid to the inverse problems (tomography) encountered in studying the double-line spectroscopic binaries

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity

Tidal Effects in Pre-merger Neutron Stars and Dynamics of Scalarized Compact Objects

In the first part of this thesis, we investigate some tidal phenomena in the pre-merger stage of coalescing binaries with at least one neutron star (NS) involved. In particular, during the last few minutes of coalescences, the tidal field exerted by the companion can force the primary strongly to excite certain quasi-normal modes thus resulting in various observable effects. Among other things, resonance of low frequency modes (e.g., $g$- and $i$-modes) may result in crustal fracture, whereby unleash the energy used to be stored in the cracked area, possibly constituting a pre-emission of short gamma-ray burst (SGRB) if the NS is highly magnetised. In particular, we find it possible to associate two pre-emissions of SGRB 090510 with the resonantly excited $g_1$- and $g_2$-modes. We present, in addition, that the inferred frequencies of these two $g$-modes provide a novel avenue to estimate the spin of the NS, which can be applied to any SGRB preceded by two or more precursors. This presumably, $g$-mode-related phenomenon can also benefit in constraining the equation of state (EOS) since the EOS candidates can be grouped in terms of $g$-mode frequency. On the other hand, $f$-mode excitation accelerates the merger course, leading to a ``tidal plunge'' phase; thereby, a phase shift is rendered in the associated gravitational waveform, which dictates the evolutionary track of the binary. Although the adiabatic tide attributes much more to the phase shift than the dynamical ones if the NS rotates slowly, the situation for fast spinning stars is different: a few hundred radiants of shift may be rendered. The second part of this thesis is dedicated to the study of the dynamics of compact objects, viz.~NSs and black holes (BHs), in alternative gravity theories in the strong gravity regime. In particular, we consider some theories involving scalar field(s) as additional mediator(s) of gravitational interaction such as the (multi-)scalar-tensor theory and scalar-Gauss-Bonnet theory. In the former theory, it can happen that the scalar field of static stars dies out in the power of $-2$ of the distance, suppressing the scalar dipole radiation thus not constrained by pulsar experiments. In addition, these solutions are of discrete topological types, characterised by topological charge. For the zero charge configurations, we show that up to three stable stars exist for a certain range of central energy density, and the stability is lost right at the occurrence of the most massive (either scalarized or non-scalarized) star. Accretions may therefore bring a stable scalarized NS into an unstable state, where a descalarization would be triggered, generating the gravitational phase transition (PT). This novel kind of PT leads to a sudden shrink in size of the star, mimicking well the traditional, material PT. However, the former transition will be accompanied by scalar-induced gravitational waves that are absent in material PT. In addition to the accreting process, we consider the spherically-symmetric core collapse for the scalar-tensor and the scalar-Gauss-Bonnet theories. Although a scalarized BH is absent in the former theory due to no-hair reason, we can construct one in the latter theory. In particular, we numerically demonstrate scalarization in a remnant BH behind stellar collapse, giving a first example on the production channel for scalarized BHs in the scalar-Guass-Bonnet theory. The scalar-induced gravitational waves generated along with (de)scalarization in both theories are also discussed

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity

New Foundation in the Sciences: Physics without sweeping infinities under the rug

It is widely known among the Frontiers of physics, that “sweeping under the rug” practice has been quite the norm rather than exception. In other words, the leading paradigms have strong tendency to be hailed as the only game in town. For example, renormalization group theory was hailed as cure in order to solve infinity problem in QED theory. For instance, a quote from Richard Feynman goes as follows: “What the three Nobel Prize winners did, in the words of Feynman, was to get rid of the infinities in the calculations. The infinities are still there, but now they can be skirted around . . . We have designed a method for sweeping them under the rug. [1] And Paul Dirac himself also wrote with similar tune: “Hence most physicists are very satisfied with the situation. They say: Quantum electrodynamics is a good theory, and we do not have to worry about it any more. I must say that I am very dissatisfied with the situation, because this so-called good theory does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it turns out to be small—not neglecting it just because it is infinitely great and you do not want it!”[2] Similarly, dark matter and dark energy were elevated as plausible way to solve the crisis in prevalent Big Bang cosmology. That is why we choose a theme here: New Foundations in the Sciences, in order to emphasize the necessity to introduce a new set of approaches in the Sciences, be it Physics, Cosmology, Consciousness etc

Laboratory-directed research and development: FY 1996 progress report

This report summarizes the FY 1996 goals and accomplishments of Laboratory-Directed Research and Development (LDRD) projects. It gives an overview of the LDRD program, summarizes work done on individual research projects, and provides an index to the projects` principal investigators. Projects are grouped by their LDRD component: Individual Projects, Competency Development, and Program Development. Within each component, they are further divided into nine technical disciplines: (1) materials science, (2) engineering and base technologies, (3) plasmas, fluids, and particle beams, (4) chemistry, (5) mathematics and computational sciences, (6) atomic and molecular physics, (7) geoscience, space science, and astrophysics, (8) nuclear and particle physics, and (9) biosciences

Microfluidics and Nanofluidics Handbook

The Microfluidics and Nanofluidics Handbook: Two-Volume Set comprehensively captures the cross-disciplinary breadth of the fields of micro- and nanofluidics, which encompass the biological sciences, chemistry, physics and engineering applications. To fill the knowledge gap between engineering and the basic sciences, the editors pulled together key individuals, well known in their respective areas, to author chapters that help graduate students, scientists, and practicing engineers understand the overall area of microfluidics and nanofluidics. Topics covered include Finite Volume Method for Numerical Simulation Lattice Boltzmann Method and Its Applications in Microfluidics Microparticle and Nanoparticle Manipulation Methane Solubility Enhancement in Water Confined to Nanoscale Pores Volume Two: Fabrication, Implementation, and Applications focuses on topics related to experimental and numerical methods. It also covers fabrication and applications in a variety of areas, from aerospace to biological systems. Reflecting the inherent nature of microfluidics and nanofluidics, the book includes as much interdisciplinary knowledge as possible. It provides the fundamental science background for newcomers and advanced techniques and concepts for experienced researchers and professionals

Gravitational Wave Signal Templates, Pattern Recognition, and Reciprocal Eulerian Gamma Functions

The direct detection of Gravitational Waves (GWs) is one of the most challenging problems in experimental gravitation today. It necessitates the use of highly advanced large laser interferometers such as LIGO, VIRGO, LISA, TAMA 300, GEO 600 and AIGO. The analysis of the data from such instruments requires and combines the expertise from a multitude of scientific disciplines. The verification of a detected signal demands an effective way to distinguish the source signal from the background noise. Such a study is required for an all-sky search to determine the @f and @q angles on the sky of gravitational wave sources and their frequencies. In this paper, we present analytical solutions and associated numerical approximations for the inner products employed in matched filtering a GW signal using templates. An exact closed-form expression for the inner products is rigourously derived using the special functions of mathematical physics. The inner products involve reciprocal Eulerian gamma functions, which occur in the study of many diverse phenomena. The spectral noise density of the VIRGO GW detector is shown to be amenable to our analysis. Spectral noise densities like those for LIGO and GEO 600, although different and in a slightly more restricted frequency band, are likewise amenable. We study numerical computation of the inner products, estimate the computational time of the solution on serial and parallel computers, and show the efficiency of the resulting algorithms. The fitting factor that indicates the goodness of fit between a signal and a template is given in closed-form and computed numerically. The numerical plots display an approximate symmetry in the template @f and @q domain