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...

We investigate the class of ultralocal metrics on the configuration space of canonical gravity. It is described by a parameter α, where α = 0.5 corresponds to general relativity. For α less than a critical value the signature is positive definite, while for all other values it is indefinite. We show that in the positive definite case gravity becomes repulsive. From the primordial helium abundan...

A new gauge theory of gravity on flat spacetime has recently been developed by Lasenby, Doran, and Gull. Einstein’s principles of equivalence and general relativity are replaced by gauge principles asserting, respectively, local rotation and global displacement gauge invariance. A new unitary formulation of Einstein’s tensor illuminates long-standing problems with energy-momentum conservation i...

Post-relativistic gravity is a hidden variable theory for general relativity. It introduces the pre-relativistic notions absolute space, absolute time, and ether as hidden variables into general relativity. Evolution is defined by the equations of general relativity and the harmonic coordinate condition interpreted as a physical equation. There are minor differences in predictions compared with...

We recast the action principle of four dimensional General Relativity so that it becomes amenable for perturbation theory which doesn’t break general covariance. The coupling constant becomes dimensionless (GNewtonΛ) and extremely small 10 . We give an expression for the generating functional of perturbation theory. We show that the partition function of quantum General Relativity can be expres...

In general relativity the gravitational field is encoded in the Riemannian geometry of space-time. Much of the conceptual compactness and mathematical elegance of the theory can be traced back to this central idea. The encoding is also directly responsible for the most dramatic ramifications of the theory: the big-bang, black holes and gravitational waves. However, it also leads one to the conc...

We propose a reformulation of general relativity by making the Abelian decomposition of Einstein’s theory. Based on the view that Einstein’s theory can be interpreted as a gauge theory of Lorentz group, we decompose the Einstein’s gravitational connection (the gauge potential of Lorentz group Γμ) into the restricted connection made of the potential of the maximal Abelian subgroup H of Lorentz g...

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...

A spacetime theory of matter, based on general relativity, is shown to provide, as a special case, standard electroweak theory.