All static spherically symmetric anisotropic solutions of Einstein's equations

An algorithm recently presented by Lake to obtain all static spherically symmetric perfect fluid solutions, is extended to the case of locally anisotropic fluids (principal stresses unequal). As expected, the new formalism requires the knowledge of two functions (instead of one) to generate all possible solutions. To illustrate the method some known cases are recovered.Comment: 8 pages Latex. To appear in Phys. Rev. D. New reference added. Some references correcte

The spacetime outside a source of gravitational radiation: The axially symmetric null fluid

We carry out a study of the exterior of an axially and reflection symmetric source of gravitational radiation. The exterior of such a source is filled with a null fluid produced by the dissipative processes inherent to the emission of gravitational radiation, thereby representing a generalization of the Vaidya metric for axially and reflection symmetric spacetimes. The role of the vorticity, and its relationship with the presence of gravitational radiation is put in evidence. The spherically symmetric case (Vaidya) is, asymptotically, recovered within the context of the $1+3$ formalism.Comment: 11 pages Latex. arXiv admin note: text overlap with arXiv:1609.02841. Typos corrected, to appear in Eur. Phys. J.