Remarks on Cosmic Strings and Quantum Gravity

Abstract

A quantum equivalence principle is formulated by means of a gravitational phase operator which is an element of the Poincare group. This is applied to the spinning cosmic string which suggests that it may, but not necessarily, contain gravitational torsion. A new exact solution of the Einstein- Cartan-Sciama-Kibble equations for the gravitational field with torsion is obtained everywhere for a cosmic string with uniform energy density, spin density and flux. The quantization condition for fluxoid due to London and DeWitt is generalized to include the spin flux. A novel effect due to the quantized gravitational field of the cosmic string on the wave function of a particle outside the string is used to show that spacetime points are not meaningful in quantum gravity.