Gravitomagnetism in superconductors and compact stars

There are three experimentally observed effects in rotating superconductors that are so far unexplained. Some authors have tried to interpret such a phenomena as possible new gravitational properties of coherent quantum systems: in particular, they suggest that the gravitomagnetic field of that kind of matter may be many orders of magnitude stronger than the one expected in the standard theory. Here I show that this interpretation would be in conflict with the common belief that neutron stars have neutrons in superfluid state and protons in superconductive one.