5 research outputs found
Dark Energy and Extending the Geodesic Equations of Motion: Connecting the Galactic and Cosmological Length Scales
Recently, an extension of the geodesic equations of motion using the Dark
Energy length scale was proposed. Here, we apply this extension to the
analyzing the motion of test particles at the galactic scale and longer. A
cosmological check of the extension is made using the observed rotational
velocity curves and core sizes of 1393 spiral galaxies. We derive the density
profile of a model galaxy using this extension, and with it, we calculate
to be ; this is within experimental error of the
WMAP value of . We then calculate to be
kpc, which is in reasonable agreement with observations.Comment: 25 pages. Accepted for publication in General Relativity and
Gravitation. Paper contains the published version of the second half of
arXiv:0711.3124v2 with corrections include
Coupling of Linearized Gravity to Nonrelativistic Test Particles: Dynamics in the General Laboratory Frame
The coupling of gravity to matter is explored in the linearized gravity
limit. The usual derivation of gravity-matter couplings within the
quantum-field-theoretic framework is reviewed. A number of inconsistencies
between this derivation of the couplings, and the known results of tidal
effects on test particles according to classical general relativity are pointed
out. As a step towards resolving these inconsistencies, a General Laboratory
Frame fixed on the worldline of an observer is constructed. In this frame, the
dynamics of nonrelativistic test particles in the linearized gravity limit is
studied, and their Hamiltonian dynamics is derived. It is shown that for
stationary metrics this Hamiltonian reduces to the usual Hamiltonian for
nonrelativistic particles undergoing geodesic motion. For nonstationary metrics
with long-wavelength gravitational waves (GWs) present, it reduces to the
Hamiltonian for a nonrelativistic particle undergoing geodesic
\textit{deviation} motion. Arbitrary-wavelength GWs couple to the test particle
through a vector-potential-like field , the net result of the tidal forces
that the GW induces in the system, namely, a local velocity field on the system
induced by tidal effects as seen by an observer in the general laboratory
frame. Effective electric and magnetic fields, which are related to the
electric and magnetic parts of the Weyl tensor, are constructed from that
obey equations of the same form as Maxwell's equations . A gedankin
gravitational Aharonov-Bohm-type experiment using to measure the
interference of quantum test particles is presented.Comment: 38 pages, 7 figures, written in ReVTeX. To appear in Physical Review
D. Galley proofs corrections adde