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Can Spacetime Curvature be Used in Future Navigation Systems?

  • Hernando QuevedoEmail author
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 196)

Abstract

We argue that the curvature generated by a gravitational field can be used to calculate the corresponding metric which determines the trajectories of freely falling test particles. To this end, we present a method to compute the metric from a given curvature tensor. We use Petrov’s classification to handle the structure and properties of the curvature tensor, and Cartan’s structure equations in an orthonormal tetrad to investigate the differential equations that relate the curvature with the metric. The second structure equation is integrated to obtain the explicit expression for the connection \(1-\)form from which the components of the orthonormal tetrad are obtained by using the first structure equation. This opens the possibility of using the curvature of astrophysical objects like the Earth to determine the position of freely falling satellites that are used in modern navigation systems.

Notes

Acknowledgements

This work has been supported by the UNAM-DGAPA-PAPIIT, Grant No. IN111617.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de MéxicoMexicoMexico
  2. 2.Dipartimento di Fisica and ICRANetUniversità di Roma “La Sapienza”RomeItaly
  3. 3.Department of Theoretical and Nuclear PhysicsKazakh National UniversityAlmatyKazakhstan

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