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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
J.L. Synge, Relativity: The General Theory (North-Holland, Amsterdam, 1960)
F.A.E. Pirani, Acta Phys. Pol. 15, 389 (1956)
P. Szekeres, J. Math. Phys. 6, 1387 (1965)
D. Puetzfeld, Y.N. Obukhov, Phys. Rev. D 93, 044073 (2016)
K.S. Thorne, C.W. Misner, J.A. Wheeler, Gravitation (W. H. Freeman, San Francisco, 1973)
R. Debever, J. Geheniau, Bull. Acad. R. Soc. Belg. 42, 114 (1956)
H. Quevedo, Gen. Relativ. Gravit. 24, 693 (1992)
M. Demiański, Phys. Lett. A 42, 157 (1972)
M. Cahen, L. Defrise, Commun. Math. Phys. 11, 16 (1968)
M. MacCallum, C. Hoenselaers, H. Stephani, D. Kramer, E. Herlt, Exact Solutions of Einstein’s Field Equations (Cambridge University Press, Cambridge, 2003)
Acknowledgements
This work has been supported by the UNAM-DGAPA-PAPIIT, Grant No. IN111617.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Quevedo, H. (2019). Can Spacetime Curvature be Used in Future Navigation Systems?. In: Puetzfeld, D., Lämmerzahl, C. (eds) Relativistic Geodesy. Fundamental Theories of Physics, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-030-11500-5_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-11500-5_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11499-2
Online ISBN: 978-3-030-11500-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)