Relativistic positioning systems: the emission coordinates

Coll, Bartolomé; Pozo, José M.

doi:10.1088/0264-9381/23/24/012

Cited by 34 publications

(55 citation statements)

References 17 publications

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“…as a physical realization of a mathematical coordinate system) [2,8], the above positioning system presents interesting qualities and, among them, those of being generic, (gravity-)free and immediate. This fact has been pointed out elsewhere [1,2,3,8] and some explicit results have been recently obtained for the generic four-dimensional case [9,10,11].…”

Section: Introductionsupporting

confidence: 58%

Positioning with stationary emitters in a two-dimensional space-time

2006

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The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D 73, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic emitters, have been considered in a flat space-time. Here, we want to show in what precise senses positioning systems allow to make relativistic gravimetry. For this purpose, we consider stationary positioning systems, constituted by two uniformly accelerated emitters separated by a constant distance, in two different situations: absence of gravitational field (Minkowski plane) and presence of a gravitational mass (Schwarzschild plane). The physical coordinate system constituted by the electromagnetic signals broadcasting the proper time of the emitters are the so called emission coordinates, and we show that, in such emission coordinates, the trajectories of the emitters in both situations, absence and presence of a gravitational field, are identical. The interesting point is that, in spite of this fact, particular additional information on the system or on the user allows not only to distinguish both space-times, but also to complete the dynamical description of emitters and user and even to measure the mass of the gravitational field. The precise information under which these dynamical and gravimetric results may be obtained is carefully pointed out.

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Section: Introductionsupporting

confidence: 58%

Positioning with stationary emitters in a two-dimensional space-time

2006

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“…A splitting of this metric can be considered, see [15], changing from the six independent components (ten components minus four gauge degrees of freedom of coordinate transformations) of AB g to a more convenient set, which neatly separates two shape parameters depending only on the direction of the covectors d A  or equivalently depending exclusively on the trajectories of the emitters, from other four scaling parameters depending on the length of the covectors or depending on the proper time of each satellite.…”

Section: Contravariant Metric In Emission Coordinatesmentioning

confidence: 99%

“…This problem has been solved for a general configuration of the emitters in flat Minkowski space-time [18,19] and also for the case of a special configuration of the emitters in a Schwarzschild spacetime [20]. However, in general the known results for the flat and curved two dimensional spacetimes are not trivially generalizable for the realistic curved four dimensional one [15] and much work remains to be done in the future.…”

Section: Realistic Four Dimensional Casesmentioning

confidence: 99%

Relativistic versus Newtonian Frames

Pascual-Sánchez¹,

Miguel²,

Vicente³

2013

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Only a causal class among the 199 Lorentzian ones, which do not exists in the Newtonian space-time, is privileged to construct a generic, gravity free and immediate (non retarded) relativistic positioning system. This is the causal class of the null emission coordinates. Emission coordinates are defined and generated by four emitters broadcasting their proper times. The emission coordinates are covariant (frame independent) and hence valid for any user. Any observer can obtain the values of his (her) null emission coordinates from the emitters which provide him his (her) position and trajectory.

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“…The hypersurface J where this Jacobian vanishes, J = {x | j Θ (x) = 0}, has been studied by Coll and Pozo [2,3] who stated that J is constituted by those events for which any user in them can see the four emitters on a circle in his celestial sphere.…”

Section: Emission Configuration Regions and Orientation Of A Positionmentioning

confidence: 99%