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17002 results

Page 131 of 851

  • 6 - Equations of Motion in the PPN Formalism

  • Clifford M. Will, University of Florida
  • Book:
    Theory and Experiment in Gravitational Physics
    Published online:
    07 September 2018
    Print publication:
    27 September 2018, pp 129-155

  • Summary

    We derive the equations of motion for a variety of physical systems in the PPN formalism, including photons, fluid systems, and N-body systems consisting of well-separated self-gravitating objects. We also specialize to two-body systems and describe the framework for calculating perturbations of Keplerian orbit elements induced by post-Newtonian corrections in the equations of motion. For a class of theories based on an invariant action, we obtain the Lagrangian that describes the dynamics of an N-body system. We derive the locally-measured, or effective gravitational constant, as measured by a Cavendish experiment, within the PPN formalism. For spinning bodies, we obtain the equations of motion and the equations of spin precession.

  • 10 - Structure and Motion of Compact Objects

  • Clifford M. Will, University of Florida
  • Book:
    Theory and Experiment in Gravitational Physics
    Published online:
    07 September 2018
    Print publication:
    27 September 2018, pp 206-231

  • Summary

    We discuss the structure of compact bodies – neutron stars and black holes – in metric theories of gravity. We give a recipe for calculating the structure of such bodies, assumed to be non-rotating for simplicity, in generic metric theories, and then describe the results of calculations in specific theories. Turning to the motion of compact bodies, we develop the modified Einstein-Infeld-Hoffmann (EIH) framework, a generalization of the post-Newtonian N-body Lagrangian to systems containing one or more compact bodies, introducing parameters that may depend upon both the theory of gravity and the internal structure of each body. We analyse a number of observable effects in binary systems containing compact bodies and obtain their dependences on these parameters. The modified EIH parameters are calculated in a number of theories of gravity, including general relativity, scalar-tensor theories and Einstein-Aether/Khronometric theories.

  • 7 - The Classical Tests

  • Clifford M. Will, University of Florida
  • Book:
    Theory and Experiment in Gravitational Physics
    Published online:
    07 September 2018
    Print publication:
    27 September 2018, pp 156-169

  • Summary

    We describe three central tests of general relativity, sometimes call the "classical" tests: the deflection of light, the Shapiro time delay and the perihelion advance of Mercury. After deriving each effect in detail within the PPN formalism, we describe the various measurements that lead to tight bounds on the relevant PPN parameters.

Theory and Experiment in Gravitational Physics
  • 2nd edition
  • Clifford M. Will
  • Published online:
    07 September 2018
    Print publication:
    27 September 2018
  • The 2015 centenary of the publication of Einstein's general theory of relativity, and the first detection of gravitational waves have focused renewed attention on the question of whether Einstein was right. This review of experimental gravity provides a detailed survey of the intensive testing of Einstein's theory of gravity, including tests in the emerging strong-field dynamical regime. It discusses the theoretical frameworks needed to analyze gravitational theories and interpret experiments. Completely revised and updated, this new edition features coverage of new alternative theories of gravity, a unified treatment of gravitational radiation, and the implications of the latest binary pulsar observations. It spans the earliest tests involving the Solar System to the latest tests using gravitational waves detected from merging black holes and neutron stars. It is a comprehensive reference for researchers and graduate students working in general relativity, cosmology, particle physics and astrophysics.

  • 11 - Interiors and atmospheres

  • Michael Perryman
  • Book:
    The Exoplanet Handbook
    Published online:
    25 August 2018
    Print publication:
    30 August 2018, pp 559-648

  • Summary

    ASIGNIFICANT ADVANCE IN THE KNOWLEDGE of exoplanet interiors and atmospheres was made possible with the discovery of transiting exoplanets. Densities derived from their masses and radii are providing some indications of their interior structure and composition, while optical and infrared transit and eclipse spectroscopy are yielding the first insights into the atmospheric composition, atmospheric dynamics, and thermal transport processes of hot Jupiters. All of this has been substantially facilitated by the knowledge of interiors and atmospheres of the solar system planets and satellites acquired over the last half century.

    The insights that can be expected from improved photometric or spectroscopic measurements, for example, with JWST due for launch in 2020, are substantial. For planets inferred to be in the ‘habitable zone’ of their host star, where liquid water is expected to be supported, diagnostics can hope to identify detailed atmospheric compositions, including signatures that may be attributable to primitive or more advanced life forms. These advances are providing a new impetus to searches for life, and even for intelligent life, and the grand question of whether life is extremely common, or extremely rare, elsewhere in the Universe.

    Introduction

    Physical models of exoplanets span two extreme classes of object, and potentially much in between: the lowmass high-density ‘solid’ planets dominated by metallic cores and silicate-rich and/or ice-rich mantles, and the high-mass low-density gas giants dominated by their massive accreted H/He envelopes.

    For the gas-rich giants, models of their interiors and models of their atmospheres are closely connected, and the most recent atmospheric models couple their emergent flux with their assembly by core accretion. Models of their interiors predict bulk properties such as the pressure–temperature relation, and their radii as a function of mass. For close-in, highly irradiated gas giants, the additional external heat source has a significant effect on the pressure–temperature structure of the outer atmosphere. Combined with inferences on their probable bulk chemical composition, atmospheric models also predict colours and spectral features arising from specific atomic and molecular species.

Page 131 of 851