Form invariance of differential equations in general relativity

Form Invariance of Differential Equations in General Relativity

Einstein equations for several matter sources in Robertson-Walker and Bianchi I type metrics, are shown to reduce to a kind of second order nonlinear ordinary differential equation ÿ + αf(y)ẏ + βf(y) ∫ f(y) dy + γf(y) = 0. Also, it appears in the generalized statistical mechanics for the most interesting value q = −1. The invariant form of this equation is imposed and the corresponding nonlocal...

Differential Forms and Wave Equations for General Relativity

Recently, Choquet-Bruhat and York and Abrahams, Anderson, ChoquetBruhat, and York (aacy) have cast the 3+1 evolution equations of general relativity in gauge-covariant and causal “first-order symmetric hyperbolic form,” thereby cleanly separating physical from gauge degrees of freedom in the Cauchy problem for general relativity. A key ingredient in their construction is a certain wave equation...

Local Scale Invariance and General Relativity

According to the theory of unimodular relativity developed by Anderson and Finkelstein, the equations of general relativity with a cosmological constant are composed of two independent equations, one which determines the null-cone structure of space-time, another which determines the measure structure of space-time. The field equations that follow from the restricted variational principle of th...

General relativity histories theory II : Invariance groups

In this paper we show in detail how the histories description of general relativity carries representations of both the spacetime diffeomorphisms group and the Dirac algebra of constraints. We show that the introduction of metric-dependent equivariant foliations leads to the crucial result that the canonical constraints are invariant under the action of spacetime diffeomorphisms. Furthermore, t...

3 + 1 General Relativity In Hyperbolic Form