Obtaining the Weyl tensor from the Bel-Robinson tensor

The algebraic study of the Bel-Robinson tensor proposed and initiated in a previous work (Gen. Relativ. Gravit. {\bf 41}, see ref [11]) is achieved. The canonical form of the different algebraic types is obtained in terms of Bel-Robinson eigen-tensors. An algorithmic determination of the Weyl tensor from the Bel-Robinson tensor is presented.Comment: 21 page

New Black Hole Solutions in Brans-Dicke Theory of Gravity

Existence check of non-trivial, stationary axisymmetric black hole solutions in Brans-Dicke theory of gravity in different direction from those of Penrose, Thorne and Dykla, and Hawking is performed. Namely, working directly with the known explicit spacetime solutions in Brans-Dicke theory, it is found that non-trivial Kerr-Newman-type black hole solutions different from general relativistic solutions could occur for the generic Brans-Dicke parameter values -5/2\leq \omega <-3/2. Finally, issues like whether these new black holes carry scalar hair and can really arise in nature and if they can, what the associated physical implications would be are discussed carefully.Comment: 20 pages, no figure, Revtex, version to appear in Phys. Rev.

Rotating metrics admitting non-perfect fluids in General Relativity

In this paper, by applying Newman-Janis algorithm in spherical symmetric metrics, a class of embedded rotating solutions of field equations is presented. These solutions admit non-perfect fluidsComment: LaTex, 39 page

On purely gravito-magnetic vacuum space-times

It is shown that there are no purely magnetic, vacuum, spacetime metrics where any one of the following conditions holds: (a) the ratio of any two eigenvalues of the Weyl tensor is constant, (b) both of the Riemann principal null directions, defining the time-like blade, are nonrotating, (c) the shear tensor possesses an eigenvector va which is defined by one of the space-like Riemann principal directions, (d) the vorticity is parallel to va, where va is defined by one of the space-like Riemann principal directions