Topics In Gravitational Dynamics

This set of lectures collects surveys of open problems in celestial dynamics and dynamical astronomy applied to solar, extra-solar and galactic systems. The discovery and thus the possibility to study many new extra-solar planetary systems have spurred new developments in the field and enabled the testing and enlargement of the domains of validity of theoretical predictions through the Nekhoroshev theorem.

This set of lectures collects surveys of open problems in celestial dynamics and dynamical astronomy applied to solar, extra-solar and galactic systems. Emphasis is on questions of stability of planetary systems. In particular the discovery and thus the possibility to study many new extra-solar planetary systems have spurred new developments in the field and enabled the testing and enlargement of the domains of validity of theoretical predictions through the Nekhoroshev theorem.

The Restless Universe: Applications of Gravitational N-Body Dynamics to Planetary Stellar and Galactic Systems stimulates the cross-fertilization of ideas, methods, and applications among the different communities who work in the gravitational N-body problem arena, across diverse fields of astrophysics. The chapters and topics cover three broad the

This work is mainly motivated by two recent crucial scientific achievements: 1) The GPS clocks, moving with earth round the sun, do not show the gravita-tional slowing by the solar field, contradicting a fundamental prediction of General Relativity (GR) and 2) The Higgs theory discloses the origin of the inertial mass of the elementary particles and hence also is responsible for the gravitational fields, because mass generates the gravitational fields. Many clear-cut experimental observations, which are in conflict with the current theories, are actually being ignored and maintained in standby by the establishment to preserve accepted theories. This is not a scientific attitude. This is religion. The only scientifically sane attitude is acknowledging the reliable experimental observations, abandoning the obsolete theories that cannot account for them and searching for a more adequate theory. This exactly is what the present work challenges to do and the results are encouraging.

Gravity plays a central role in the dynamics of all astrophysical systems - from stars to the Universe as a whole. This timely volume examines all aspects of gravitational dynamics - from stellar systems and galaxy disks, to the dynamics of the Local Group, large scale structures and motions, galaxy formation and general relativity. Each chapter is written by a world expert renowned for original contributions to the field. The authors are: James Binney, Roger Blandford, David Burstein, Tim de Zeeuw, George Efstathiou, Steve Gull, Nick Kaiser, J. Katz, Donald Lynden-Bell, Ruth Lynden-Bell, Douglas Lin, Jeremiah Ostriker, T. Padmanabhan, J. Papaloizou, Jim Peebles, Jim Pringle, Martin Rees, Maarteen Schmidt, Scott Tremaine and Simon White. This volume provides a broad, pedagogical introduction to gravitational dynamics for graduate students, and an up-to-date review for researchers in cosmology, astrophysics, mathematical physics and applied mathematics.

In their search for solutions to problems concerning the dynamics of the Earth as a self-gravitating body, the authors have applied the fundamentals found in their book “Jacobi Dynamics” (1987, Reidel). First, satellite observations have shown that the Earth does not remain in hydrostatic equilibrium, which forms the physical basis of modern geodynamics. Secondly, satellite data have established a relationship between the planet’s polar moment of inertia and the potential of the Earth’s outer force field, which proves the most basic point of Jacobi dynamics. This allowed the authors to revise their derivation of the classical virial theorem, introducing the concept of a volumetric force and volumetric moment, and so to obtain a generalized virial theorem in the form of Jacobi’s equation. The main dynamical effects are: the kinetic energy of oscillation of the interacting particles, which explains the physical meaning and nature of gravitational forces; separation of shells of a self-gravitating body with respect to its mass density; differences in angular velocities of the shell’s rotation; continuity in variance of the potential of the outer gravitational force field, together with reductions in the envelope of the interacting masses (volumetric center of gravity); the nature of Earth, Moon and satellite precession; the nature and generating mechanism of the planet’s electromagnetic field; the common nature of gravitational and electromagnetic energy, and other related issues. The work is a logical continuation of the book "Jacobi Dynamics" and is intended for researchers, teachers and students engaged in theoretical and experimental research in various branches of astronomy, geophysics, planetology and cosmogony, and for students of celestial, statistical, quantum and relativistic mechanics and hydrodynamics.

Proceedings from the 2012 Fourth International Meeting on Gravitation and Cosmology, focusing on accelerated cosmic expansion This volume provides both an update and a review of the state of alternative theories of gravity in connection with the accelerated expansion of the universe issue. Different theoretical proposals exist to explain the acceleration in the cosmic expansion, generating the dark energy issue and opening the possibility to theories of gravity alternative to general relativity. Related issues such as the dark matter problem are also surveyed in order to give the readers profound insight on the subject from different points of view. Comprised of short talks and plenary lectures given by leading experts in the field, some of them with brilliant and historic contributions, the book allows the reader to find readable and referenced surveys in topics like f(R) theories, the dark matter and dark energy issues, Modified Newtonian Dynamics (MOND) scenarios, f(T) theories, scalar-tensor theories derived from non-Riemannian geometries, emergent universes, the cosmological constant and other topics of current interest for younger and senior physicists and graduate students. These proceedings are from the Fourth International Meeting on Gravitation and Cosmology, held in Guadalajara, Jalisco, México, from 20 - 25 May, 2012, was sponsored by ICTP- Trieste, Italy and COECyTJAL-Universidad de Guadalajara, México. This event is a series of scientific meetings started in 2004 in Cuba, focusing on current and selected topics in the fields of gravitation and cosmology.

Covering all aspects of gravitation in a contemporary style, this advanced textbook is ideal for graduate students and researchers in all areas of theoretical physics. The 'Foundation' section develops the formalism in six chapters, and uses it in the next four chapters to discuss four key applications - spherical spacetimes, black holes, gravitational waves and cosmology. The six chapters in the 'Frontier' section describe cosmological perturbation theory, quantum fields in curved spacetime, and the Hamiltonian structure of general relativity, among several other advanced topics, some of which are covered in-depth for the first time in a textbook. The modular structure of the book allows different sections to be combined to suit a variety of courses. Over 200 exercises are included to test and develop the reader's understanding. There are also over 30 projects, which help readers make the transition from the book to their own original research.