Let (M,g,Ω) be the conformal rescaling of a 3+1 dimensional vacuum spacetime (M̃, g̃), with g = Ωg̃, where Ω is a smooth function on M vanishing on the boundary ∂M. If M has smooth null boundary I , with connected components of topology S2×R, it follows that the Weyl tensor of (M,g) vanishes on I . From this follows peeling properties for (M̃, g̃). This picture of isolated systems in general relativ...

A new development of the “monodromy transform” method for analysis of hyperbolic as well as elliptic integrable reductions of Einstein equations is presented. Compatibility conditions for some alternative representations of the fundamental solutions of associated linear systems with spectral parameter in terms of a pair of dressing (“scattering”) matrices give rise to a new set of linear (quasi...

Solutions of Einstein vacuum equations, for a static pseudospherically symmetric system, are presented. They describe a naked singularity and a singular solution with many resemblances to the Schwartzschild solution but with two major differences: its static region, lying inside the null horizon, sees the singularity, and its effective gravitational field is repulsive. We shortly discuss on the...

The paper proposes an amendment to the relativistic continuum mechanics which introduces relationship between density tensors and curvature of spacetime. resulting formulation a symmetric stress–energy tensor for system with electromagnetic field leads solution Einstein Field Equations indicating metric tensor. In this EFE solution, cosmological constant is related invariant tensor, additional ...

Along the general framework of the gauge invariant perturbation theory developed in the papers [K. Nakamura, Prog. Theor. Phys. 110 (2003), 723; ibid, 113 (2005), 481.], we rederive the second-order Einstein equations on four-dimensional homogeneous isotropic background universe in gauge-invariant manner without ignoring any mode of perturbations. We consider the perturbations both in the unive...

I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled variables, the so-called “conformal field equations” developed by Friedrich. These equations allow to include “infinity” on a finite grid, solving regular equations, ...