Gravity of Monopole and String and Gravitational Constant in 3He-A

Abstract

We discuss the effective metric produced in superfluid 3He-A by such topological objects as radial disgyration and monopole. In relativistic theories these metrics are similar to that of the local string and global monopole correspondingly. But in 3He-A they have the negative angle deficit, which corresponds to the negative mass of the topological objects. The effective gravitational constant G in superfluid 3He-A, derived from the comparison with relativistic theories, is inversely proportional to the square of the gap amplitude Delta, which plays the part of the Planck energy cut-off. G depends on temperature and increases with T, which corresponds to the vacuum screening of the Newton's constant.