Abstract
The Newtonian equations of motion, and Newton's law of gravitation can be obtained by a limit\(\lambda = \frac{1}{{c^2 }} \to 0\) of Einstein's equations. For a sufficiently small constant Λ the existence of a set of solutions (0≤λ≤Λ) of Einstein's equations of a stationary, axisymmetric star is proven. This existence is proven in weighted Sobolev spaces with the implicit function theorem. Since the value of the causality constant λ depends only on the units used to measure the velocity, the existence of a solution for any small λ is physically interesting.
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Communicated by S.-T. Yau
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Heilig, U. On the existence of rotating stars in general relativity. Commun.Math. Phys. 166, 457–493 (1995). https://doi.org/10.1007/BF02099884
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DOI: https://doi.org/10.1007/BF02099884