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The critical condition, eq. (22), has been derived from eq. (20) which, however, uses an incorrect limit. The correct limit is
where T1 and φ1 are the temperature and the gravitational potential at the boundary of the self-gravitating system, respectively. We assume that these limits do not change with temperature. This yields
Using this expression in eqs. (15) and (18), eq. (20) can be written as
which now correctly leads to expression (22).