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We consider ideal fluid and equivalent scalar field dark energy universes where all four known types of finite time, future singularities occur at some parameter values. It is demonstrated that pressure/energy density of such quintessence/phantom dark energy diverges in spherically-symmetric spacetime at finite radius or at the center. This may cause the instability of the relativistic star or black hole in such universe. The resolution of the problem via the extra modification of the equation of state is briefly discussed.
Nojiri et al. (2009) studied this question.