Comparison of String Fluid Dynamical Models in General Relativity and Einstein–Cartan theory

Abstract

Dynamical models of string fluids areconstructed from the general energy-momentum tensor forstring fluids in general relativity and theEinstein-Cartan theories obtained from the Ray-Hilbertvariational principle. Examples of solutions to the fieldequations for general relativistic spacetimes are givenand compared with solutions obtained from the postulatedenergy-momentum tensor of Letelier. Solutions to the field equations in Riemann-Cartanspacetimes are compared with an extended Leteliersolution. All calculations are given for both thestandard and the extended thermodynamics versions inwhich the latter includes the string as thermodynamicvariables. In general relativity, it is shown for blackhole solutions that the general feature of strings(through the string vector) is to produce a shrinkage of the black hole horizon. In RiemannCartanspacetimes, the torsion field equation shows that stringvector can be identified with the torsion vector. Themost striking feature of strings in Riemann-Cartan spacetimes is that in the Reissner-Nordstromsolution, the addition of torsional strings produces thecorrect asympototic behavior of the metric necessary tomatch the experimental galactic rotationcurves.