We have applied the numerical method which was developed for Newtonian gravity to general relativistic, differentially rotating bodies including ring-like structures. A number of equilibrium structures are obtained for two different polytropic indices N = 1/2 and N = 3/2, because the various proposed equations of state for the nuclear density region fall into the range N = 1/2 to 3/2 from the viewpoint of its softness. Each modelled sequence is specified by three parameters: the polytropic index N, the strength of gravity |κ=pₘax/εₘaxc²| and the rotation parameter A. Here pmax is the maximum pressure, εmax the maximum energy density. For a large value of A, the rotation law approaches that for a rigid rotation. For a small value of A, the rotation law becomes that for j-constant rotation, where j is the specific angular momentum measured by the proper time of matter. We have computed 10 sequences for N = 3/2 polytropes and 9 sequences for N = 1/2 polytropes with various values of κ and A. For both the strong (general relativistic) and weak (Newtonian) gravities, models including two limiting cases of nearly rigid rotation and strongly differential rotation are obtained. We have found (i) that the non-dimensional quantity |F=(J6-2N/KN)1/(10-4N)/M| is a good parameter to classify the equilibrium structures, where J is the total angular momentum, M the gravitational mass and K the polytropic constant, (ii) that the ratio of the rotational to the gravitational energy T/|W| increases as κ becomes large for the same value of F, and (iii) that the increase in the gravitational mass by rotation is considerably suppressed in the strong-gravity limit.
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Komatsu et al. (1989) studied this question.