Recently, non-standard Lagrangians have gained a growing importance in theoretical physics and in the theory of non-linear differential equations. However, their formulations and implications in general relativity are still in their infancies despite some advances in contemporary cosmology. The main aim of this paper is to fill the gap. Though non-standard Lagrangians may be defined by a multit...

The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a complex Hermitian, nonsymmetric gμν and discuss the problems associated with such a theory. We then introduce a complex symmetric (non-Hermitian) metric, with...

A relativistic modified gravity (MOG) called Scalar-Tensor-Vector Gravity (STVG) desribes a self-consistent, stable gravity theory that contains Einstein’s general relativity in a well-defined limit. The theory has an extra degree of freedom, a vector field called a “phion” field whose curl is a skew symmetric field that couples to matter (“fifth force”). The spacetime geometry is described by ...

It is known that, in string sigma-model metric, the 'extreme' fivebrane solution of D=10 supergravity interpolates between D=10 Minkowski spacetime and a supersym-metric S 3 compactification to a linear dilaton vacuum. We show here that, in fivebrane sigma-model metric, the extreme string solution of D=10 supergravity interpolates between Minkowski spacetime and a hitherto unknown supersymmetri...

In a series of recent papers we developed formulation general relativity in which spacetime and the dynamics matter evolve with Poincaré invariant parameter τ. this paper, apply formalism to derive metric induced by ‘static’ event evolving uniformly along its t-axis at spatial origin x=0. The is shown vary t τ, as well distance r, taking maximum value for test particle retarded time τ=t−r/c. re...