A model is proposed in which the Hawking particles emitted by a black hole are treated as an envelope of matter that obeys an equation of state, and acts as a source in Einsteins equations. This is a crude but interesting way to accommodate for the back reaction. For large black holes, the solution can be given analytically, if the equation of state is $p=kapparho$, with $0<kappa<1$. The solution exhibits a singularity at the origin. If we assume $N$ free particle types, we can use a Hartree-Fock procedure to compute the contribution of one such field to the entropy, and the result scales as expected as $1/N$. A slight mismatch is found that could be attributed to quantum corrections to Einsteins equations, but can also be made to disappear when $k$ is set equal to one. The case $kappa=1$ is further analysed.
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