Abstract

It is argued that under a natural hypothesis the fermions inside a black hole formed after the collapse of a neutron star could form a noncompressible fluid (well before reaching the Planck scale) leading to some features of the integer quantum Hall effect. The relations with black hole entropy are analyzed. Insights coming from the quantum Hall effect are used to analyze the coupling with the Einstein equations. Connections with some cosmological scenarios and with the higher dimensional quantum Hall effect are briefly pointed out. © 2007 The American Physical Society.