ar X iv : h ep - t h / 96 03 07 7 v 1 1 2 M ar 1 99 6 Gravitational Meissner Effect

The gravitational analogue of the electromagnetic Meissner effect is investigated. Starting from the post-Newtonian approximation to general relativity we arrive at gravitational London equations, predicting a grav-itational Meissner effect. Applied to neutron stars we arrive at a London penetration depth of 12km, which is about the size of a neutron star. There is strong evidence that neutron stars are superfluid and maybe super-conducting [1], indicating that macroscopic quantum effects play a significant role in neutron stars. In addition neutron stars are very strongly gravitating objects. We therefore would like to investigate the possibility of macroscopic quantum gravity effect in the form of a gravitational Meissner effect. In the post-Newtonian approximation Einstein's theory of general relativ-ity, gravity looks like a U(1) theory and is very similar to the electromagnetic Maxwell theory [2]. This allows us to follow closely the approach of London [3, 4] in deriving gravitational London equations, predicting a gravitational Meissner effect. Not knowing the underlying microscopic theory of quantum gravity we have to resort to this semi-classical approach. We find the gravitational London penetration depth to be about 12 km for a typical neutron star of radius 15 km. Furthermore, as the density of the neutron star increases, the London penetration depth decreases, suggesting that quantum gravity aspects may become significant as the neutron star approaches collapse. Macroscopic quantum aspects are best described by a BCS type theory[5]. However, since BCS needs a quantum theory of the underlying interaction, and since we do not have a microscopic theory of quantum gravity at this moment,