Weak-Field Gravity of Revolving Circular Cosmic Strings
  A weak-field solution of Einstein's equations is constructed. It is generated by a circular cosmic string revolving in its plane about the centre of the circle. (The revolution is introduced to prevent the string from collapsing.) This solution exhibits a conical singularity, and the corresponding deficit angle is the same as for a straight string of the same linear energy density, irrespective of the angular velocity of the string. 
Des J. Mc Manus and Michel A. Vandyck