Fermi-Frenet coordinates for space-like curves

@article{Underwood2007FermiFrenetCF,
  title={Fermi-Frenet coordinates for space-like curves},
  author={Michael S. Underwood and Karl-Peter Marzlin},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2007}
}
We generalize Fermi coordinates, which correspond to an adapted set of coordinates describing the vicinity of an observer's worldline, to the worldsheet of an arbitrary spatial curve in a static spacetime. The spatial coordinate axes are fixed using a covariant Frenet triad so that the metric can be expressed using the curvature and torsion of the spatial curve. As an application of Fermi-Frenet coordinates, we show that they allow covariant inertial forces to be expressed in a simple and… 
10 Citations
Wavefronts of traveling trajectories of geometric particles
  • W. Bi, Zhigang Wang
  • Mathematics
    International Journal of Geometric Methods in Modern Physics
  • 2019
Confining the traveling trajectory of a tachyon to the two-dimensional Lorentzian space forms, we describe the trajectory as a spacelike front in these Lorentzian space forms. Introducing the
Geometrical particles and dualities related to curves in null de Sitter 3-sphere
  • Xue Song, D. Pei
  • Mathematics
    International Journal of Modern Physics A
  • 2021
In this paper, we confine the trajectory of geometrical particles to the de Sitter three-dimensional space–time, we model geometrical particles as spacelike tachyons. Using the Legendrian duality
Singularities of worldsheets associated with null Cartan curves in Lorentz–Minkowski space–time
In this paper, as applications of singularity theory, we study the singularities of several worldsheets generated by null Cartan curves in Lorentz–Minkowski space–time. Using the approach of the
Is torsion needed in a theory of gravity? A reappraisal
It is known that General Relativity ({\bf GR}) uses a Lorentzian Manifold $(M_4;g)$ as a geometrical model of the physical spacetime. The metric $g$ is required to satisfy Einstein's equations. Since
Landau's problem in the noncommutative quantum mechanics and linearized gravitational waves: DeWitt's approach
We present a systematic study of the noncommutative interaction of gravitational waves with matter at the quantum mechanical level in the long wavelength and small velocity limit. In particular, the
Singularities of worldsheets in spherical space–times
In this paper, the singularities of the geometry for four classes of worldsheets, which are respectively, located in three-dimensional hyperbolic space and three-dimensional de Sitter space–time are
Recognition of singularities of rectifying worldsheets generated by framed worldlines
In this paper, we consider the local topological structures of a class of new worldsheets, call it the rectifying worldsheets, which are generated by a class of singular worldlines. Using the
Hyperbolic worldsheets and worldlines of null Cartan curves in de Sitter 3-space
The hyperbolic worldsheets and the hyperbolic worldline generated by null Cartan curves are defined and their geometric properties are investigated. As applications of singularity theory, the singu...
An Interactive Lane Change Decision Making Model With Deep Reinforcement Learning
TLDR
Experimental results demonstrate the capability of the proposed model to execute lane change maneuver with comfortable and safety reference trajectory at an appropriate time instance and traffic gap in various highway traffic scenarios.
لوا رابتعا ضرف اب
  • Business
  • 2020
هدیکچ نادیم هیرظن ،ربو شور ۀیاپ رب نادیم و رلاکسا یاه رد یموتناوک یاه ار نامیر شمخ روسنات زا لوا بیرقت رد و دلیشتراوش کیرتم یم یسیونزاب نمتب شور زا هدافتسا اب و نادیم تکرح ۀلداعم زا عورش اب .مینک –

References

SHOWING 1-10 OF 21 REFERENCES
Fermi coordinates for weak gravitational fields.
  • Marzlin
  • Physics
    Physical review. D, Particles and fields
  • 1994
TLDR
The Fermi coordinate system of an observer in arbitrary motion in an arbitrary weak gravitational field valid to all orders in the geodesic distance from the world line of the observer is derived to make the correspondence between general relativity and Newtonian gravity more precise.
Fermi Normal Coordinates and Some Basic Concepts in Differential Geometry
Fermi coordinates, where the metric is rectangular and has vanishing first derivatives at each point of a curve, are constructed in a particular way about a geodesic. This determines an expansion of
The physical meaning of Fermi coordinates
Fermi coordinates (FC) are supposed to be the natural extension of Cartesian coordinates for an arbitrary moving observer in curved space-time. Since their construction cannot be done on the whole
Optical reference geometry for stationary and static dynamics
Attention is drawn to the advantages of representing dynamical behavior in a stationary or static background spacetime in terms of a fixed reference 3-geometry that differs from the usual one by a
ABSOLUTE AND RELATIVE FRENET-SERRET FRAMES AND FERMI-WALKER TRANSPORT
Relative Frenet-Serret 3-frames are defined along a test particle worldline with respect to a family of observers and a corresponding comoving relative Frenet-Serret 3-frame is introduced in the
Inertial and gravitational effects in the proper reference frame of an accelerated, rotating observer
Most experimental laboratories accelerate and rotate relative to inertial frames. This paper derives approximate expressions for the general-relativistic metric and the general-relativistic equations
Inertial effects of a Dirac particle.
  • Hehl, Ni
  • Physics
    Physical review. D, Particles and fields
  • 1990
TLDR
The effects found include the Bonse-Wroblewski phase shift due to acceleration, the Sagnac-type effect, the rotation-spin effect, and the redshift of the kinetic energy.
What is the reference frame of an accelerated observer
MAXWELL‐Theorie (in Medien) und Quantentheorie in einem rotierenden Bezugssystem
On the basis of our 3-dimensional conceptions of the electromagnetic quantities [1] the MAXWELL theory is represented in a rotating frame of reference. For such a frame the MAXWELL equations obtain
Gravitational perturbation of the hydrogen spectrum
The perturbations of the energy levels of a freely falling one-electron atom in an arbitrary external gravitational field are considered. The energy-level shifts are calculated to first order in the
...
...