We show that the Gödel type Metrics in three dimensions with arbitrary two dimensional background space satisfy the Einstein-perfect fluid field equations identically. There exists only one first order partial differential equation satisfied by the components of fluid’s velocity vector field. We then show that the same metrics solve the field equations of the topologically massive gravity where...

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now propose a variational principle for Evans’ theory and show that it yields two field equations. The second field equation is algebraic in the torsion...

We consider the interaction between perturbations in the inflaton and in the metric during the preheating phase in simple inflationary models. By numerically integrating the Einstein field equations we are able to gauge the impact of non-linear gravitational effects on preheating for the first time. In the λφ model we find a large increase in the amplitude of sub-Hubble metric modes, beyond tha...

The Einstein field equations for several cosmological models reduce to polynomial systems of ordinary differential equations. In this paper we shall concentrate our attention to the spatially homogeneous diagonal G2 cosmologies. By using Darboux’s theory in order to study ordinary differential equations in the complex projective plane CP we solve the Bianchi V models totally. Moreover, we carry...

The theory of the Relativistic Schrödinger Equations is further developped and extended to non-linear field equations. The technical advantage of the Relativistic Schrödinger approach is demonstrated explicitly by solving the coupled Einstein-Klein-Gordon equations including a non-linear Higgs potential in case of a Robertson-Walker universe. The numerical results yield the effect of dynamical ...

• The history of the equations of gravitational field is of particular interest because they are related to two famous names: Albert Einstein and David Hilbert, and because the circumstances of their invention bear sometimes almost detective character. One of the early references is the book " Einstein, Hilbert and the Theory of Gravitation " by a renowned historian of science J. Mehra [1], whe...

It is folklore that Albert Einstein’s greatest blunder occurred in 1917 when he introduced the cosmological constant term into his theory of general relativity [5]. At the time Einstein believed the universe to be static, and yet his original field equations, which describe how the gravitational influence of matter bends space-time, predicted an expanding (or contracting) one. To resolve this a...

We study gravitational theory in 1 + 2 spacetime dimensions which is determined by the Lagrangian constructed as a sum of the Einstein-Hilbert term plus the two (translational and rotational) gravitational Chern-Simons terms. When the corresponding coupling constants vanish, we are left with the purely Einstein theory of gravity. We obtain new exact solutions for the gravitational field equatio...

The Chevreton superenergy tensor was introduced in 1964 as a counterpart, for electromagnetic fields, of the well-known Bel-Robinson tensor of the gravitational field. We here prove the unnoticed facts that, in the absence of electromagnetic currents, Chevreton’s tensor (i) is completely symmetric, and (ii) has a trace-free divergence if Einstein-Maxwell equations hold. It follows that the trac...

The construction of gravitational wave observatories is one of the greatest scientific efforts of our time. As a result, there is presently a strong need to numerically simulate the emission of gravitation radiation from massive astronomical events such as black hole collisions. This entails the numerical solution of the Einstein field equations. We briefly describe the field equations in their...