TUNED STRING GEOMETRIES FOR STATIONARY GRAVITATIONAL-FIELDS

It is shown that a static equilibrium state of a general elastic string model (of the category that includes models appropriate for the description of superconducting cosmic strings) with respect to a stationary background spacetime is a geodesic with respect to a certain Riemannian metric on the quotient space with respect to the stationary action. In terms of a system of the standard kind with ignorable time coordinate xo and space coordinates xR the required 'string metric' will be given in terms of the ordinary spacetime metric components by an expression of the form (T/T o)2(goRgoS-goog RS) where To is a scale constant and T is a scalar field giving the local string tension as a certain function of gOO, the form of this function being determined by the relevant equation of state and by an adjustable 'tuning parameter', mu o.