Incompressible fluid inside an astrophysical black hole?

It is argued that under natural hypothesis the Fermions inside a black hole formed after the collapse of a neutron star could form a non compressible fluid (well before reaching the Planck scale) leading to some features of integer Quantum Hall Effect. The relations with black hole entropy are analyzed. Insights coming from Quantum Hall Effect are used to analyze the coupling with Einstein equations. Connections with some cosmological scenarios and with higher dimensional Quantum Hall Effect are shortly pointed out.