132 research outputs found
Mach's Principle and the Origin of Inertia
The current status of Mach's principle is discussed within the context of
general relativity. The inertial properties of a particle are determined by its
mass and spin, since these characterize the irreducible unitary representations
of the inhomogeneous Lorentz group. The origin of the inertia of mass and
intrinsic spin are discussed and the inertia of intrinsic spin is studied via
the coupling of intrinsic spin with rotation. The implications of spin-rotation
coupling and the possibility of history dependence and nonlocality in
relativistic physics are briefly mentioned.Comment: 14 pages. Dedicated to Carl Brans in honor of his 80th birthday. To
appear in the Brans Festschrift; v2: typo corrected, published in: At the
Frontier of Spacetime, edited by T. Asselmeyer-Maluga (Springer, 2016),
Chapter 10, pp. 177-18
New Upper Limit of Terrestrial Equivalence Principle Test for Rotating Extended Bodies
Improved terrestrial experiment to test the equivalence principle for
rotating extended bodies is presented, and a new upper limit for the violation
of the equivalence principle is obtained at the level of 1.6, which is limited by the friction of the rotating gyroscope. It
means the spin-gravity interaction between the extended bodies has not been
observed at this level.Comment: 4 page
Effects of Space-Time Curvature on Spin-1/2 Particle Zitterbewegung
This paper investigates the properties of spin-1/2 particle Zitterbewegung in
the presence of a general curved space-time background described in terms of
Fermi normal co-ordinates, where the spatial part is expressed using general
curvilinear co-ordinates. Adopting the approach first introduced by Barut and
Bracken for Zitterbewegung in the local rest frame of the particle, it is shown
that non-trivial gravitational contributions to the relative position and
momentum operators appear due to the coupling of Zitterbewegung frequency terms
with the Ricci curvature tensor in the Fermi frame, indicating a formal
violation of the weak equivalence principle. Explicit expressions for these
contributions are shown for the case of quasi-circular orbital motion of a
spin-1/2 particle in a Vaidya background. Formal expressions also appear for
the time-derivative of the Pauli-Lubanski vector due to space-time curvature
effects coupled to the Zitterbewegung frequency. As well, the choice of
curvilinear co-ordinates results in non-inertial contributions in the time
evolution of the canonical momentum for the spin-1/2 particle, where
Zitterbewegung effects lead to stability considerations for its propagation,
based on the Floquet theory of differential equations.Comment: 22 pages, no figures; slight revisions; accepted for publication in
Classical and Quantum Gravit
Tidal Dynamics in Kerr Spacetime
The motion of free nearby test particles relative to a stable equatorial
circular geodesic orbit about a Kerr source is investigated. It is shown that
the nonlinear generalized Jacobi equation can be transformed in this case to an
autonomous form. Tidal dynamics beyond the critical speed c/sqrt(2) is studied.
We show, in particular, that a free test particle vertically launched from the
circular orbit parallel or antiparallel to the Kerr rotation axis is tidally
accelerated if its initial relative speed exceeds c/sqrt(2). Possible
applications of our results to high-energy astrophysics are briefly mentioned.Comment: 15 pages, 3 figures; v2: slightly expanded version accepted for
publication in CQ
Gauge-Dependent Cosmological "Constant"
When the cosmological constant of spacetime is derived from the 5D
induced-matter theory of gravity, we show that a simple gauge transformation
changes it to a variable measure of the vacuum which is infinite at the big
bang and decays to an astrophysically-acceptable value at late epochs. We
outline implications of this for cosmology and galaxy formation.Comment: 14 pages, no figures, expanded version to be published in Class.
Quantum Gra
Spacetime Splitting, Admissible Coordinates and Causality
To confront relativity theory with observation, it is necessary to split
spacetime into its temporal and spatial components. The (1+3) timelike
threading approach involves restrictions on the gravitational potentials
, while the (3+1) spacelike slicing approach involves
restrictions on . These latter coordinate conditions protect
chronology within any such coordinate patch. While the threading coordinate
conditions can be naturally integrated into the structure of Lorentzian
geometry and constitute the standard coordinate conditions in general
relativity, this circumstance does not extend to the slicing coordinate
conditions. We explore the influence of chronology violation on wave motion. In
particular, we consider the propagation of radiation parallel to the rotation
axis of stationary G\"odel-type universes characterized by parameters and such that for ) chronology is
protected (violated). We show that in the WKB approximation such waves can
freely propagate only when chronology is protected.Comment: 25 pages, 3 figures; v2: minor typos corrected, accepted for
publication in Phys. Rev.
Angular momentum effects in Michelson-Morley type experiments
The effect of the angular momentum density of a gravitational source on the
times of flight of light rays in an interferometer is analyzed. The calculation
is made imagining that the interferometer is at the equator of the gravity
source and, as long as possible, the metric, provided it is stationary and
axisymmetric, is not approximated. Finally, in order to evaluate the size of
the effect in the case of the Earth a weak field approximation is introduced.
For laboratory scales and non-geodesic paths the correction turns out to be
comparable with the sensitivity expected in gravitational waves interferometric
detectors, whereas it drops under the threshold of detectability when using
free (geodesic) light rays.Comment: 12 pages, LaTeX; more about the detection technique, references
added; accepted for publication in GR
The Sagnac Effect in curved space-times from an analogy with the Aharonov-Bohm Effect
In the context of the natural splitting, the standard relative dynamics can
be expressed in terms of gravito-electromagnetic fields, which allow to
formally introduce a gravito-magnetic Aharonov-Bohm effect. We showed elsewhere
that this formal analogy can be used to derive the Sagnac effect in flat
space-time as a gravito-magnetic Aharonov-Bohm effect. Here, we generalize
those results to study the General Relativistic corrections to the Sagnac
effect in some stationary and axially symmetric geometries, such as the
space-time around a weakly gravitating and rotating source, Kerr space-time,
G\"{odel} universe and Schwarzschild space-time.Comment: 14 pages, 1 EPS figure, LaTeX, accepted for publication in General
Relativity and Gravitatio
On the possibility of measuring the Earth's gravitomagnetic force in a new laboratory experiment
In this paper we propose, in a preliminary way, a new Earth-based laboratory
experiment aimed to the detection of the gravitomagnetic field of the Earth. It
consists of the measurement of the difference of the circular frequencies of
two rotators moving along identical circular paths, but in opposite directions,
on a horizontal friction-free plane in a vacuum chamber placed at South Pole.
The accuracy of our knowledge of the Earth's rotation from VLBI and the
possibility of measuring the rotators'periods over many revolutions should
allow for the feasibility of the proposed experiment.Comment: Latex2e, 8 pages, no figures, no tables, accepted for publication by
Classical and Quantum Gravity. Typo corrected in the formula of the error in
the difference of the orbital period
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
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