Abstract
We present a variational theory for the trajectories of a massive, charged particle in a relativistic spacetime with an electromagnetic field. We state some result on the existence and the multiplicity of such trajectories joining two points, assuming that the spacetime is standard stationary and the electromagnetic field is constant with respect to the standard time coordinate. The results are obtained using critical point theory for functionals on infinite dimensional manifolds and the topological properties of the spacetime.
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References
Beem, J.K., Ehrlich, P.E., Easley, K.L. (1996): Global Lorentzian Geometry. 2nd Edition. Marcel Dekker, New York-Basel
O’Neill, B. (1983): Semiriemannian Geometry with Applications to Relativity. Academic Press, New York
Hawking, S.W., Ellis, G.F.R. (1972): The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge
Masiello, A. (2000): Applications of Calculus of Variations to General Relativity, in Recent Developments in General Relativity, 13th Italian Conference on General Relativity and Gravitational Physics, Monopoli, Italy, September 18–22, 1998, ed. by B. Casciaro, D. Fortunato, M. Francaviglia, A. Masiello. Springer-Verlag, Milano, pp. 173–195
Landau, L., Lifschitz, L. (1970): Théorie des Champs. Mir, Moscow
Thirring, W. (1992): Classical Mathematical Physics. Springer-Verlag, Berlin Heidelberg New York
Benci, V, Fortunato, D. (1998): Found. Phys. 26, 333
Masiello, A. (1994): Variational Methods in Lorentzian Geometry. Pitman Research Notes in Mathematics 309 Longman, London
Caponio, E., Masiello, A. (2001): Non linear analysis, in press
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Caponio, E., Masiello, A. (2002). Trajectories for Relativistic Particles in an Electromagnetic Field. In: Cianci, R., Collina, R., Francaviglia, M., Fré, P. (eds) Recent Developments in General Relativity, Genoa 2000. Springer, Milano. https://doi.org/10.1007/978-88-470-2101-3_28
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DOI: https://doi.org/10.1007/978-88-470-2101-3_28
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-0162-6
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