Abstract
In these lectures we shall derive the Einstein field and the equations of motion for uncharged and charged self- gravitating fluids from variational principles. We shall also see how singular hyper-surfaces (shock waves) and the equations governing their behavior may be treated by means of these principles. In addition we shall show how the “second variation” problem is related to the discussion of the stability of the solutions of the Einstein field equations.
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References
Chandrasekhar, S. The dynamical instability of gaseous masses approaching the Schwarzschild limit in general relativity. Astrophys. J. 140, 417–433 (1964).
Taub, A.H. Small motions of a spherically symmetric distribution of matter. Les Theories Relativistes de la Graviation, pp. 173–191. Centre National de la Recherches Scientific, Paris (1962).
Singular hypersurfaces in general relativity, Illinois J. Math. 1, 370–388 (1957.
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Taub, A.H. (2011). Variational Principles In General Relativity. In: Cattaneo, C. (eds) Relativistic Fluid Dynamics. C.I.M.E. Summer Schools, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11099-3_3
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DOI: https://doi.org/10.1007/978-3-642-11099-3_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11097-9
Online ISBN: 978-3-642-11099-3
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