478 research outputs found
Binary spinning black hole Hamiltonian in canonical center-of-mass and rest-frame coordinates through higher post-Newtonian order
The recently constructed Hamiltonians for spinless binary black holes through
third post-Newtonian order and for spinning ones through formal second
post-Newtonian order, where the spins are counted of zero post-Newtonian order,
are transformed into fully canonical center-of-mass and rest-frame variables.
The mixture terms in the Hamiltonians between center-of-mass and rest-frame
variables are in accordance with the relation between the total linear momentum
and the center-of-mass velocity as demanded by global Lorentz invariance. The
various generating functions for the center-of-mass and rest-frame canonical
variables are explicitly given in terms of the single-particle canonical
variables. The no-interaction theorem does not apply because the world-line
condition of Lorentz covariant position variables is not imposed.Comment: 18 pages, no figure
Prospects in the orbital and rotational dynamics of the Moon with the advent of sub-centimeter lunar laser ranging
Lunar Laser Ranging (LLR) measurements are crucial for advanced exploration
of the laws of fundamental gravitational physics and geophysics. Current LLR
technology allows us to measure distances to the Moon with a precision
approaching 1 millimeter. As NASA pursues the vision of taking humans back to
the Moon, new, more precise laser ranging applications will be demanded,
including continuous tracking from more sites on Earth, placing new CCR arrays
on the Moon, and possibly installing other devices such as transponders, etc.
Successful achievement of this goal strongly demands further significant
improvement of the theoretical model of the orbital and rotational dynamics of
the Earth-Moon system. This model should inevitably be based on the theory of
general relativity, fully incorporate the relevant geophysical processes, lunar
librations, tides, and should rely upon the most recent standards and
recommendations of the IAU for data analysis. This paper discusses methods and
problems in developing such a mathematical model. The model will take into
account all the classical and relativistic effects in the orbital and
rotational motion of the Moon and Earth at the sub-centimeter level. The new
model will allow us to navigate a spacecraft precisely to a location on the
Moon. It will also greatly improve our understanding of the structure of the
lunar interior and the nature of the physical interaction at the core-mantle
interface layer. The new theory and upcoming millimeter LLR will give us the
means to perform one of the most precise fundamental tests of general
relativity in the solar system.Comment: 26 pages, submitted to Proc. of ASTROCON-IV conference (Princeton
Univ., NJ, 2007
Post-Newtonian Theory for Precision Doppler Measurements of Binary Star Orbits
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 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
, 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 , 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, . We briefly discuss feasibility of
practical implementation of these theoretical results, which crucially depends
on further progress in the technique of precision Doppler measurements.Comment: Minor changes, 1 Figure included, submitted to Astrophys.
Horava-Lifshitz gravity: tighter constraints for the Kehagias-Sfetsos solution from new solar system data
We analytically work out the perturbation induced by the Kehagias-Sfetsos
(KS) space-time solution of the Horava-Lifshitz (HL) modified gravity at long
distances on the two-body range for a pair of test particles A and B orbiting
the same mass M. We apply our results to the most recently obtained
range-residuals \delta\rho for some planets of the solar system (Mercury, Mars,
Saturn) ranged from the Earth to effectively constrain the dimensionsless KS
parameter \psi_0 for the Sun. We obtain \psi_0 >= 7.2 x 10^-10 (Mercury),
\psi_0 >= 9 x 10^-12 (Mars), \psi_0 >= 1.7 x 10^-12 (Saturn). Such lower bounds
are tighter than other ones existing in literature by several orders of
magnitude. We also preliminarily obtain \psi_0 >= 8 x 10^-10 for the system
constituted by the S2 star orbiting the Supermassive Black Hole (SBH) in the
center of the Galaxy.Comment: LaTex2e, 15 pages, 1 table, 3 figures, 31 references. Version
matching the one at press in International Journal of Modern Physics D
(IJMPD
Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers
General relativistic deflection of light by mass, dipole, and quadrupole
moments of gravitational field of a moving massive planet in the Solar system
is derived. All terms of order 1 microarcsecond are taken into account,
parametrized, and classified in accordance with their physical origin. We
calculate the instantaneous patterns of the light-ray deflections caused by the
monopole, the dipole and the quadrupole moments, and derive equations
describing apparent motion of the deflected position of the star in the sky
plane as the impact parameter of the light ray with respect to the planet
changes due to its orbital motion. The present paper gives the physical
interpretation of the observed light-ray deflections and discusses the
observational capabilities of the near-future optical (SIM) and radio (SKA)
interferometers for detecting the Doppler modulation of the radial deflection,
and the dipolar and quadrupolar light-ray bendings by the Jupiter and the
Saturn.Comment: 33 pages, 10 figures, accepted to Phys. Rev.
Uniqueness of collinear solutions for the relativistic three-body problem
Continuing work initiated in an earlier publication [Yamada, Asada, Phys.
Rev. D 82, 104019 (2010)], we investigate collinear solutions to the general
relativistic three-body problem. We prove the uniqueness of the configuration
for given system parameters (the masses and the end-to-end length). First, we
show that the equation determining the distance ratio among the three masses,
which has been obtained as a seventh-order polynomial in the previous paper,
has at most three positive roots, which apparently provide three cases of the
distance ratio. It is found, however, that, even for such cases, there exists
one physically reasonable root and only one, because the remaining two positive
roots do not satisfy the slow motion assumption in the post-Newtonian
approximation and are thus discarded. This means that, especially for the
restricted three-body problem, exactly three positions of a third body are true
even at the post-Newtonian order. They are relativistic counterparts of the
Newtonian Lagrange points L1, L2 and L3. We show also that, for the same masses
and full length, the angular velocity of the post-Newtonian collinear
configuration is smaller than that for the Newtonian case. Provided that the
masses and angular rate are fixed, the relativistic end-to-end length is
shorter than the Newtonian one.Comment: 18 pages, 1 figure; typos corrected, text improved; accepted by PR
Note on the generalized Hansen and Laplace coefficients
Recently, Breiter et al (2004) reported the computation of Hansen
coefficients for non integer values of . In fact, the
Hansen coefficients are closely related to the Laplace , and
generalized Laplace coefficients (Laskar and Robutel, 1995)
that do not require to be integers. In particular, the coefficients
X_0^{\g,m} have very simple expressions in terms of the usual Laplace
coefficients b_{\g+2}^{(m)}, and all their properties derive easily from the
known properties of the Laplace coefficients.Comment: 9/11/200
Accelerating relativistic reference frames in Minkowski space-time
We study accelerating relativistic reference frames in Minkowski space-time
under the harmonic gauge. It is well-known that the harmonic gauge imposes
constraints on the components of the metric tensor and also on the functional
form of admissible coordinate transformations. These two sets of constraints
are equivalent and represent the dual nature of the harmonic gauge. We explore
this duality and show that the harmonic gauge allows presenting an accelerated
metric in an elegant form that depends only on two harmonic potentials. It also
allows reconstruction of the spatial structure of the post-Galilean coordinate
transformation functions relating inertial and accelerating frames. The
remaining temporal dependence of these functions together with corresponding
equations of motion are determined from dynamical conditions, obtained by
constructing the relativistic proper reference frame of an accelerated test
particle. In this frame, the effect of external forces acting on the observer
is balanced by the fictitious frame-reaction force that is needed to keep the
test particle at rest with respect to the frame, conserving its relativistic
linear momentum. We find that this approach is sufficient to determine all the
terms of the coordinate transformation. The same method is then used to develop
the inverse transformations. The resulting post-Galilean coordinate
transformations extend the Poincar\'e group on the case of accelerating
observers. We present and discuss the resulting coordinate transformations,
relativistic equations of motion, and the structure of the metric tensors
corresponding to the relativistic reference frames involved.Comment: revtex4, 21 page
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