Aether theory is introduced to implement the violation of the Lorentz invariance in general relativity. For this purpose a unit timelike vector field is introduced to the theory in addition to the metric tensor. Aether theory contains four free parameters which satisfy some inequalities in order that the theory to be consistent with the observations. We show that the Gödel type of metrics of ge...

In this paper, a procedure which gives Euclidean solutions of 3-dimensional Einstein-Yang-Mills equations when one has solutions of the Einstein equations is proposed. The method is based on reformulating Yang-Mills theory in such a way that it becomes a gravity. It is applied to find black hole solutions of the coupled Einstein Yang-Mills equations.

It is developed a generalized geometric method for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. Firstly, we apply the formalism of nonholonomic frame deformations (formally considered for nonholonomic manifolds and Finsler spaces) when the gravitational field equations transform into systems of nonlinear partial differential equations whi...

This is a comment on a reply to a comment on a paper of Hellaby & Dray, repeating the identification of an important mistake which is still being denied by the authors: their proposed solutions do not satisfy the Einstein-Klein-Gordon equations at a change of signature. Substitution of the proposed solutions into the Einstein-Klein-Gordon equations in unit normal coordinates yields Dirac δ term...

Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to ...

We consider the Einstein/Yang-Mills equations in 3 + 1 space time dimensions with SU(2) gauge group and prove rigorously the existence of a globally defined smooth static solution. We show that the associated Einstein metric is asymp-totically flat and the total mass is finite. Thus, for non-abelian gauge fields the Yang/Mills repulsive force can balance the gravitational attractive force and p...

No Kerr-like exact solution has yet been found in Chern-Simons modified gravity. Intrigued by this absence, we study stationary and axisymmetric metrics that could represent the exterior field of spinning black holes. For the standard choice of the background scalar, the modified field equations decouple into the Einstein equations and additional constraints. These constraints eliminate essenti...

It is shown that under the post-Newtonian approximation the Einstein equations can be reduced to the standard Maxwell-type field equations in a medium; in such a context the Cerenkov emission by a neutral particle gives large energy loss while the particle moves at faster than the phase speed of waves in the medium. It has often been noted that magnetism can be understood as the consequence of ...