Mathematics
Scientific paper
Feb 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980gregr..12..155k&link_type=abstract
General Relativity and Gravitation, vol. 12, Feb. 1980, p. 155-174. Natural Sciences and Engineering Research Council
Mathematics
15
Balls, Fluids, Gravitational Effects, Relativity, Space-Time Functions, Asymptotic Methods, Banach Space, Einstein Equations, Equations Of State, Linear Equations, Manifolds (Mathematics)
Scientific paper
The paper demonstrates that a family of static perfect fluid solutions with fixed total gravitational mass and fixed equation of state must consist of solutions diffeomorphic to the spherically symmetric one if it depends differentiably on a parameter and contains the spherically symmetric solution. The static deformation method used by Kuenzle (1971) is used, and field equations formulated in a three-dimensional form, stating the conditions of the asymptotic behavior and the uniqueness of the spherically symmetric solutions. Finally, Fischer and Marsden's work on linearization stability (1974, 1975) is applied by considering the solution set of these equations with their boundary conditions as the inverse image of zero of a nonlinear differential operator mapping of a set of 3-metrics and potentials into a set of Y symmetric covariant tensors and functions.
Kuenzle H. P.
Savage J. R.
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