The accretion of phantom fields by black holes within a thermodynamic context is addressed. For a fluid violating the dominant energy condition, case of a phantom fluid, the Euler and Gibbs relations permit two different possibilities for the entropy and temperature: a situation in which the entropy is negative and the temperature is positive or vice-versa. In the former case, if the generalized second law (GSL) is valid, then the accretion process is not allowed whereas in the latter, there is a critical black hole mass below which the accretion process occurs. In a universe dominated by a phantom field, the critical mass drops quite rapidly with the cosmic expansion and black holes are only slightly affected by accretion. All black holes disappear near the big rip, as suggested by previous investigations, if the GSL is violated.
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