A new version of nonsymmetric gravitational theory is presented. The field equations are expanded about the Minkowski metric, giving in lowest order the linear Einstein field equations and massive Proca field equations for the antisymmetric field g [µν]. An expansion about an arbitrary Einstein background metric yields massive Proca field equations with couplings to only physical modes. It foll...

There exist different methods to find the solutions of the Einstein–Maxwell equations [1]. Some high symmetry solutions of the Einstein equations have direct astrophysical or cosmological interpretation [2]. In [3], a new conjecture was formulated which says: “ A test electromagnetic field having a potential proportional to the Killing vector of a seed vacuum gravitational field (up to a consta...

Sometimes the most obvious questions are the most fruitful ones. The Zurich Notebook is a case in point. The notebook shows that Einstein already considered the field equations of general relativity about three years before he published them in November 1915. In the spring of 1913 he settled on different equations, known as the “ Entwurf ” field equations after the title of the paper in which t...

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

The theory of evolution equations has been applied in various ways in general relativity. Following some general considerations about this, some illustrative examples of the use of ordinary differential equations in general relativity are presented. After this recent applications of Fuchsian equations are described, with particular attention to work on the structure of singularities of solution...