Physics
Scientific paper
Feb 1966
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1966pthph..35..241s&link_type=abstract
Progress of Theoretical Physics, Vol. 35, No. 2, pp. 241-260
Physics
7
Scientific paper
The instability criterion for a star without rotation is derived by the method of variation, in the post-Newtonian approximation, and proved to coincide with the results of Chandrasekhar's paper. To apply this criterion to the supermassive stars, we have calculated the adiabatic exponent in the case of electron pair creation, and obtained the following results: The instability results from the general relativistic effect for stars of M > 3.5\cdot 10^4M_{odot}, and from electron pair creation for M < 3.5\cdot 10^4M_{odot}. The applicability of our treatments is limited to 10^9M_{odot} > M > 10^3M_{odot}: The upper limit results from the fact that a star above this limit cannot be in quasi-static equilibrium but must be in free fall contraction, and the lower limit results from our assumption about the structure, which takes a simple polytrope of index 3.
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