Static Solutions of the Einstein Equations for Spherically Symmetric Elastic Bodies
نویسنده
چکیده
We analyze the Einstein equations for a spherically symmetric static distribution of matter which satisfies a given constitutive relation for elastomechanics. After reducing the equations into a system of Fuchsian ODE for certain scalar invariants of the strain, we show that, for a given constitutive relation and a given value of central pressure satisfying certain compatibility conditions, there exists a unique regular solution near the center. In the case when the constitutive relation is given by a quadratic form of strain, we further show that the solutions stay regular up to the boundary of the material ball. † Current Address: 134 Ivy Dr. Apt.5, Charlottesville, VA 22903, U.S.A.
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