Rapidly rotating polytropes in the post-Newtonian approximation to general relativity |
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| Authors: | G G Fahlman S P S Anand |
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| Institution: | (1) David Dunlap Observatory, University of Toronto, Ont., Canada;(2) Present address: Institute of Theoretical Astronomy, University of Cambridge, Cambridge, England |
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| Abstract: | The study of uniformly polytropes with axial symmetry is extended to include all rotational terms of order  4, where is the angular velocity, consistently within the first post-Newtonian approximation to general relativity. The equilibrium structure is determined by treating the effects of rotation and post-Newtonian gravitation as independent perturbations on the classical polytropic structure. The perturbation effects are characterized by a rotation parameter  = 2/2 G
c
and a relativity parameter,  =p
c
/
c
C
2
, wherep
c
and c are the central pressure and density respectively. The solution to the structural problem is obtained by following Chandrasekhar's series expansion technique and is complete to the post-Newtonian rotation terms of order
2. The critical rotation parameterv
c
, which characterizes the configuration with maximum uniform rotation, is accurately evaluated as a function of . Numerical values for all the structural parameters needed to determine the equilibrium configurations are presented for polytropes with indicesn=1, 1.5, 2, 2 5, 3, and 3.5. |
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| Keywords: | |
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