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Leonid M Ozernoy - One of the best experts on this subject based on the ideXlab platform.

  • post Newtonian Theory for precision doppler measurements of binary star orbits
    The Astrophysical Journal, 1999
    Co-Authors: S M Kopeikin, Leonid M Ozernoy
    Abstract:

    The determination of velocities of stars from precise Doppler measurements is described here using a relativistic Theory of astronomical reference frames to determine the Keplerian and post-Keplerian parameters of binary systems. Seven reference frames are introduced: (1) the proper frame of a particle emitting light, (2) the star-centered reference frame, (3) the barycentric frame of the binary, (4) the barycentric frame of the Galaxy, (5) the barycentric frame of the solar system, (6) the geocentric frame, and (7) the topocentric frame of observer at the Earth. We apply successive Lorentz transformations and the relativistic equation of light propagation to establish the exact treatment of Doppler effect in binary systems both in special and general relativity theories. As a result, the Doppler shift is a sum of (1) linear in c-1 terms, which include the ordinary Doppler effect and its variation due to the secular radial acceleration of the binary with respect to observer; (2) terms proportional to c-2, which include the contributions from the quadratic Doppler effect caused by the relative motion of binary star with respect to the solar system, the motion of the particle emitting light and diurnal rotational motion of observer, orbital motion of the star around the binary's barycenter, and the orbital motion of the Earth; and (3) terms proportional to c-2, which include the contributions from redshifts due to gravitational fields of the star, the star's companion, the Galaxy, the solar system, and the Earth. After parameterization of the binary's orbit, we find that the presence of periodically changing terms in the Doppler shift enables us to disentangle different terms and measure, along with the well-known Keplerian parameters of the binary, four additional post-Keplerian parameters, which characterize (1) the relativistic advance of the periastron; (2) a combination of the quadratic Doppler and gravitational shifts associated with the orbital motion of the primary relative to the binary's barycenter and the companion's gravitational field, respectively; (3) the amplitude of the "gravitational lensing" contribution to the Doppler shift; and (4) the usual inclination angle of the binary's orbit, i. We briefly discuss the feasibility of practical implementation of these theoretical results, which crucially depends on further progress in the technique of precision Doppler measurements.

  • post Newtonian Theory for precision doppler measurements of binary star orbits
    arXiv: Astrophysics, 1998
    Co-Authors: S M Kopeikin, Leonid M Ozernoy
    Abstract:

    The determination of velocities of stars from precise Doppler measurements is described here using relativistic Theory of astronomical reference frames so as to determine the Keplerian and post-Keplerian parameters of binary systems. We apply successive Lorentz transformations and the relativistic equation of light propagation to establish the exact treatment of Doppler effect in binary systems both in special and general relativity theories. As a result, the Doppler shift is a sum of (1) linear in $c^{-1}$ terms, which include the ordinary Doppler effect and its variation due to the secular radial acceleration of the binary with respect to observer; (2) terms proportional to $c^{-2}$, which include the contributions from the quadratic Doppler effect caused by the relative motion of binary star with respect to the Solar system, motion of the particle emitting light and diurnal rotational motion of observer, orbital motion of the star around the binary's barycenter, and orbital motion of the Earth; and (3) terms proportional to $c^{-2}$, which include the contributions from redshifts due to gravitational fields of the star, star's companion, Galaxy, Solar system, and the Earth. After parameterization of the binary's orbit we find that the presence of periodically changing terms in the Doppler schift enables us disentangling different terms and measuring, along with the well known Keplerian parameters of the binary, four additional post-Keplerian parameters, including the inclination angle of the binary's orbit, $i$. We briefly discuss feasibility of practical implementation of these theoretical results, which crucially depends on further progress in the technique of precision Doppler measurements.

Eric Poisson - One of the best experts on this subject based on the ideXlab platform.

  • gravitomagnetic love tensor of a slowly rotating body post Newtonian Theory
    Physical Review D, 2020
    Co-Authors: Eric Poisson
    Abstract:

    How tidally deformable bodies, such as neutron stars, couple to gravitomagnetic tidal forces is the subject of this paper. The coupling was thought to be through a scalar quantity called the Love number, but the present work shows that the assumptions in the literature that led to this identification are erroneous and the correct way to characterize the interaction is through a tensor quantity that the author calls a Love tensor. This surprising and fundamental result is derived in post-Newtonian Theory but is, in all likelihood, generalizable to full general relativity.

  • Gravity: Newtonian, Post-Newtonian, Relativistic
    2014
    Co-Authors: Eric Poisson, Clifford M. Will
    Abstract:

    Preface 1. Foundations of Newtonian gravity 2. Structure of self-gravitating bodies 3. Newtonian orbital dynamics 4. Minkowski spacetime 5. Curved spacetime 6. Post-Minkowskian Theory: formulation 7. Post-Minkowskian Theory: implementation 8. Post-Newtonian Theory: fundamentals 9. Post-Newtonian Theory: system of isolated bodies 10. Post-Newtonian celestial mechanics, astrometry and navigation 11. Gravitational waves 12. Radiative losses and radiation reaction 13. Alternative theories of gravity References Index.

Bernd G. Schmidt - One of the best experts on this subject based on the ideXlab platform.

  • Static, Self-Gravitating Elastic Bodies
    Proceedings of the Royal Society of London. Series A: Mathematical Physical and Engineering Sciences, 2003
    Co-Authors: Robert Beig, Bernd G. Schmidt
    Abstract:

    There is proved an existence theorem, in the Newtonian Theory, for static, self-gravitating bodies composed of elastic material. The theorem covers the case where these bodies are small, but allows them to have arbitrary shape.

  • Self-gravitating Fluid Shells and Their Nonspherical Oscillations in Newtonian Theory
    The Astrophysical Journal, 1999
    Co-Authors: Jiří Bičák, Bernd G. Schmidt
    Abstract:

    We summarize the general formalism describing surface flows in three-dimensional space in a form which is suitable for various astrophysical applications. We then apply the formalism to the analysis of nonradial perturbations of self-gravitating spherical fluid shells. Spherically symmetric gravitating shells (or bubbles) have been used in numerous model problems especially in general relativity and cosmology. A radially oscillating shell was recently suggested as a model for a variable cosmic object. Within Newtonian gravity we show that self-gravitating static fluid shells are unstable with respect to linear nonradial perturbations. Only shells (bubbles) with a negative mass (or with a charge the repulsion of which is compensated by a tension) are stable.

Bangalore Suryanarayana Sathyaprakash - One of the best experts on this subject based on the ideXlab platform.

  • Comparison of post-Newtonian mode amplitudes with numerical relativity simulations of binary black holes
    Classical and Quantum Gravity, 2020
    Co-Authors: Ssohrab Borhanian, K. G. Arun, Harald P. Pfeiffer, Bangalore Suryanarayana Sathyaprakash
    Abstract:

    Gravitational waves from the coalescence of two black holes carry the signature of the strong field dynamics of binary black holes. In this work we have used numerical relativity simulations and post-Newtonian Theory to investigate this dynamics. Post-Newtonian Theory is a low-velocity expansion that assumes the companion bodies to be point-particles, while numerical relativity treats black holes as extended objects with horizons and fully captures their dynamics. There is a priori no reason for the waveforms computed using these disparate methods to agree with each other, especially at late times when the black holes move close to the speed of light. We find, remarkably, that the leading order amplitudes in post-Newtonian Theory agree well with the full general relativity solution for a large set of spherical harmonic modes, even in the most dynamical part of the binary evolution, with only some modes showing distinctly different behavior than that found by numerical relativity simulations. In particular, modes with spherical harmonic indices l = m as well as l = 2, m = 1 are least modified from their dominant post-Newtonian behavior. Understanding the nature of these modes in terms of the post-Newtonian description will aid in formulating better models of the emitted waveforms in the strong field regime of the dynamics.

  • Parametrized tests of post-Newtonian Theory using Advanced LIGO and Einstein Telescope
    Physical Review D, 2010
    Co-Authors: Chandra Kant Mishra, K. G. Arun, Bala R. Iyer, Bangalore Suryanarayana Sathyaprakash
    Abstract:

    General relativity has very specific predictions for the gravitational waveforms from inspiralling compact binaries obtained using the post-Newtonian (PN) approximation. We investigate the extent to which the measurement of the PN coefficients, possible with the second generation gravitational-wave detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and the third generation gravitational-wave detectors such as the Einstein Telescope (ET), could be used to test post-Newtonian Theory and to put bounds on a subclass of parametrized-post-Einstein theories which differ from general relativity in a parametrized sense. We demonstrate this possibility by employing the best inspiralling waveform model for nonspinning compact binaries which is 3.5PN accurate in phase and 3PN in amplitude. Within the class of theories considered, Advanced LIGO can test the Theory at 1.5PN and thus the leading tail term. Future observations of stellar mass black hole binaries by ET can test the consistency between the various PN coefficients in the gravitational-wave phasing over the mass range of 11-44M(circle dot). The choice of the lower frequency cutoff is important for testing post-Newtonian Theory using the ET. The bias in the test arising from the assumption of nonspinning binaries is indicated.

  • Testing post-Newtonian Theory with gravitational wave observations
    Classical and Quantum Gravity, 2006
    Co-Authors: K. G. Arun, Bala R. Iyer, Moh’d S. S. Qusailah, Bangalore Suryanarayana Sathyaprakash
    Abstract:

    The Laser Interferometric Space Antenna (LISA) will observe supermassive black hole binary mergers with an amplitude signal-to-noise ratio of several thousand. We investigate the extent to which such observations afford high-precision tests of Einstein's gravity. We show that LISA provides a unique opportunity to probe the nonlinear structure of post-Newtonian Theory both in the context of general relativity and its alternatives.

Christian Corda - One of the best experts on this subject based on the ideXlab platform.

  • The Advance of Planets' Perihelion in Newtonian Theory Plus Gravitational and Rotational Time Dilation
    2020
    Co-Authors: Christian Corda
    Abstract:

    It is shown through three different approaches that, contrary to a longstanding conviction older than 160 years, the orbit of Mercury behaves as required by Newton's equations with a very high precision if one correctly analyzes the situation in the framework of the two-body problem without neglecting the mass of Mercury. General relativity remains more precise than Newtonian physics, but the results in this paper show that Newtonian framework is more powerful than researchers and astronomers were thinking till now, at least for the case of Mercury. The Newtonian formula of theadvance of planets' perihelion breaks down for the other planets. The predicted Newtonian result is indeed too strong for Venus and Earth. Therefore, it is also shown that corrections due to gravitational and rotational time dilation, in an intermediate framework which analyzes gravity between Newton and Einstein, solve the problem. By adding such corrections, a result consistent with the one of general relativity is indeed obtained. Thus, the most important results of this paper are two: i) It is not correct that Newtonian Theory cannot predict the anomalous rate of precession of the perihelion of planets' orbit. The real problem is instead that a pure Newtonian prediction is too strong. ii) Perihelion's precession can be achieved with the same precision of general relativity by extending Newtonian gravity through the inclusion of gravitational and rotational time dilation effects. This second result is in agreement with a couple of recent and interesting papers of Hansen, Hartong and Obers. Differently from such papers, in the present work the importance of rotational time dilation is also highlighted.

  • Solution to the Advance of the Perihelion of Mercury in Newtonian Theory
    viXra, 2020
    Co-Authors: Christian Corda
    Abstract:

    It is shown through three different approaches that, contrary to a long-standing conviction more than 160 years long, the orbit of Mercury behaves as required by Newton’s equations with a very high precision if one correctly analyses the situation in the framework of the two-body problem without neglecting the mass of Mercury. General relativity remains more precise than Newtonian physics, but the results in this paper show that Newtonian framework is more powerful than researchers and astronomers were thinking till now.