Spinning string fluid dynamics in general relativity

Abstract

The general, energy - momentum tensor for a dynamical, spinning string fluid in general relativity is presented using the Ray - Hilbert variational principle. The calculations are given for both the standard and the extended thermodynamics versions in which the latter includes both the spin and string as thermodynamic variables. Both versions yield the same Fermi - Walker transport of the spin with a correction term due to the string. As an unexpected general feature, it is shown that the string and spin are dual 2-forms. Examples of solutions to the field equations are given for the extension of static black holes for non-spinning, string fluids to stationary, slowly rotating black holes for spinning string fluids. These solutions are then compared with solutions obtained from the postulated energy - momentum tensor of Letelier. The general feature of these solutions for positive density is that the spin causes the event horizon for the stationary black hole to contract whether or not the spin is considered as a thermodynamic variable.