We investigate the geometry of a twisting non-shearing congruence null geodesics on conformal manifold even dimension greater than four and Lorentzian signature. give necessary sufficient condition Weyl tensor for twist to induce an almost Robinson structure, that is, screen bundle is equipped with complex structure. In this case, (local) leaf space acquires partially integrable contact CR stru...

The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is shown that in certain Einstein spaces one can use a conformal Killing-Yano t...

In this paper, we import tensor index notation including Einstein summation notation into programming by introducing two kinds of functions, tensor functions and scalar functions. Tensor functions are functions that contract the tensors given as an argument, and scalar functions are the others. As with ordinary functions, when a tensor function obtains a tensor as an argument, the tensor functi...

‎the notion of quasi-einstein metric in physics is equivalent to the notion of ricci soliton in riemannian spaces‎. ‎quasi-einstein metrics serve also as solution to the ricci flow equation‎. ‎here‎, ‎the riemannian metric is replaced by a hessian matrix derived from a finsler structure and a quasi-einstein finsler metric is defined‎. ‎in compact case‎, ‎it is proved that the quasi-einstein met...

We derive the general Σ2×S solution of topologically massive gravity in vacuum and in presence of a cosmological constant. The field equations reduce to three-dimensional Einstein equations and the solution has constant Ricci tensor. We briefly discuss the emergence of non-Ricci flat solutions when spin is introduced. Pac(s) numbers: 04.50.+h, 04.20.Cv, 04.20.Jb Keyword(s): Alternative theories...

Five-dimensional Einstein-Maxwell-Chern-Simons equations are investigated in the framework of an extended Kerr-Schild strategy to search for black holes solutions. The fulfillment Einstein constrains Chern-Simons coupling constant a value determined by trace energy-momentum tensor electromagnetic configuration.

Exhaustive ghost solutions to Einstein-Weyl equations for two dimensional spacetimes are obtained, where the ghost neutrinos propagate in the background spacetime, but do not influence the background spacetime due to the vanishing stress-energy-momentum tensor for the ghost neutrinos. Especially, those non-trivial ghost solutions provide a counterexample to the traditional claim that the Einste...