Abstract
We define curves on a Riemannian manifold as integrals of generalized Jacobi fields. We show that the force term that deviates the trajectory from the geodesic motion can be constructed as a functional of the metric tensor. These curves can be interpreted as particles (observers) coupled nonminimally with gravitation that can provide a class of residual observers for the inevitable singularity—as shown in the text.
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References
Hawking, S. W., and Ellis, G. F., (1973).The Large Scale Structure of Space-Time. (Cambridge University Press, Cambridge). See also references therein.
Ellis, G. F., (1971).Relativistic Cosmology, in:General Relativity and Cosmology, Rendiconti S. I. F., ed. Sachs, R. XLVIII Corso (Academic Press, New York).
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Novello, M., Galvão, A. P., Soares, I. D., and Salim, J. M. (1976). “Electric and Magnetic Gravitational Monopoles,”J. Phys. A: Math. Gen,9, 547.
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This essay received an honorable mention (1976) from the Gravity Research Foundation-Ed.
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Novello, M., Soares, I.D. & Salim, J.M. On Jacobi fields. Gen Relat Gravit 8, 95–102 (1977). https://doi.org/10.1007/BF00770728
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DOI: https://doi.org/10.1007/BF00770728