Rotating AdS-Einstein universes from constrained metrics

The imposition of a constraint between the metric tensor elements in both three- and four-dimensional, rotating anti–de Sitter (AdS) space-times is shown to reduce the number of independent equations of motion and to result in new families of solutions to the equations of motion. For the geometries investigated, analytic solutions or partial analytic solutions of the equations of motion are obtained. In all cases, the number of independent field equations is less than the number of independent functions, resulting in an undetermined function which can be freely specified. For rotating, asymptotically AdS space-times, the reduction of the number of field equations to be solved holds for vacuum black hole solutions and for black hole solutions obtained from space-times containing matter.

Figure 1

$A(r,p)$ as a function of $r$ for $p=0.3$, $\alpha =1$, $\beta =1/9$, $\kappa =0.01$, and $\omega =-1$. $A(r,p)$ vanishes at $r=1.08$. As $r$ approaches infinity, $A(r,p)\to r^2$.