Abstract
In [I, 2], the most general solution to Einstein's equations was studied in the case of small angular velocities (the ~ approximation), which is equivalent to the gravtational energy of the star being many times greater than the rotational energy: B = ~2/8~GPc << i (Pc is the density at the center of the configuration). In this approximation, the diagonal components of the metric tensor outside the mass distribution keep their Schwarzschild form, and there is also a nondiagonal component g03 = (iJ/r) sin 2 8, where J is the total angular momentum. This approximation corresponds to considering rotation of a sphere with allowance for Coriolis forces without change in its shape. The solution depends on the two mass and angular momentum parameters and can obviously be obtained from the Kerr solution [3] by expanding the latter in a series in the angular momentum and retaining the terms linear in J.
Published Version
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