1. Some Spinor-Curvature Identities - Nester, James M.; Tung, Roh Suan; Zhytnikov, Vadim V.
We describe a class of spinor-curvature identities which exist for Riemannian or Riemann-Cartan geometries. Each identity relates an expression quadratic in the covariant derivative of a spinor field with an expression linear in the curvature plus an exact differential. Certain special cases in 3 and 4 dimensions which have been or could be used in applications to General Relativity are noted.
- 24-mar-2007

2. Invariant construction of solutions to Einstein`s field equations - LRS perfect fluids I - Marklund, Mattias
The properties of some locally rotationally symmetric (LRS) perfect fluid space-times are examined in order to demonstrate the usage of the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives for finding solutions to Einstein's field equations. A new method is introduced, which makes it possible to choose the coordinates at any stage of the calculations. Three classes are examined, one with fluid rotation, one with spatial twist in the preferred direction and the space-time homogeneous models. It is also shown that there are no LRS space-times with dependence on one null coordinate. Using an extension of the method, we...
- 08-mar-2007

3. Invariant construction of solutions to Einstein's field equations - LRS perfect fluids II - Marklund, M.; Bradley, M.
The properties of LRS class II perfect fluid space-times are analyzed using the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives. In this manner it is straightforward to obtain the plane and hyperbolic analogues to the spherical symmetric case. For spherically symmetric static models the set of equations is reduced to the Tolman-Oppenheimer-Volkoff equation only. Some new non-stationary and inhomogeneous solutions with shear, expansion, and acceleration of the fluid are presented. Among these are a class of temporally self-similar solutions with equation of state given by $p=(\gamma-1)\mu, 1<\gamma<2$, and a class of solutions characterized by $\sigma=-\Theta/6$. We give an example...
- 09-mar-2007