Related papers: On conformally flat and type N pure radiation metr…
We establish an exact bidirectional map between interior Friedmann density of a collapsing star and exterior static spherically symmetric metric in generalized Oppenheimer-Snyder collapse. This reduces Einstein's differential…
The conformal Einstein equations for a tracefree (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de…
The classical Bondi-Penrose approach to the gravitational radiation theory in asymptotically flat spacetimes is recalled and recent advances in the proofs of the existence of such spacetimes are briefly reviewed. We then mention the unique…
The $\gamma$-metric, also known as Zipoy-Voorhees spacetime, is a static, axially symmetric vacuum solution to Einstein's field equations characterized by two parameters: mass and the deformation parameter $\gamma$. It reduces to the…
We analyze a class of exact type II solutions of the Robinson-Trautman family which contain pure radiation and (possibly) a cosmological constant. It is shown that these spacetimes exist for any sufficiently smooth initial data, and that…
A general form of a metric preserving all symmetries of a spherically symmetric gravitational field and angular momentum in spherical coordinates is obtained. Such metric may have $g_{01}(r)\neq 0$. The Newtonian limit uniquely defines…
We study conformal transformations in the most general parity-preserving models of the New General Relativity type. Then we apply them to analysis of cosmological perturbations in the (simplest) spatially flat cosmologies. Strong coupling…
We investigate the gravitational radiation produced by a linearly accelerated source in general relativity. The investigation is performed by studying the vacuum C metric, which is interpreted as representing the exterior space-time of an…
We consider the evolution of a flat Friedmann-Roberstson-Walker Universe in a higher derivative theories, including $\alpha R^{2}$ terms to the Einstein-Hilbert action in the presence of a variable gravitational and cosmological constants.…
Five classes of radiative solutions of Einstein's field equations are discussed in the light of some new developments. These are plane waves and their collisions, cylindrical waves, Robinson-Trautman and type N spacetimes, boost-rotation…
The well-known treatment of asymptotically flat vacuum fields is adapted to pure radiation fields. In this approach we find a natural normalization of the radiation null vector. The energy balance at null infinity shows that the mass loss…
A particular yet large class of non-diverging solutions which admits a cosmological constant, electromagnetic field, pure radiation and/or general non-null matter component is explicitly presented. These spacetimes represent exact…
We obtain a coordinate independent algorithm to determine the class of conformal Killing vectors of a locally conformally flat $n$-metric $\gamma$ of signature $(r,s)$ modulo conformal transformations of $\gamma$. This is done in terms of…
We study the gravitational wave memory effect in spacetimes related to flat space by a conformal transformation. The discussion is general but the gravitational wave length scale is assumed to be small compared with the background curvature…
Let $R$ be a constant. Let $\mathcal{M}^R_\gamma$ be the space of smooth metrics $g$ on a given compact manifold $\Omega^n$ ($n\ge 3$) with smooth boundary $\Sigma $ such that $g$ has constant scalar curvature $R$ and $g|_{\Sigma}$ is a…
We study gravitational radiation for a positive value of the cosmological constant $\Lambda$. We rely on two battle-tested procedures: (i) We start from the same null coordinate system used by Bondi and Sachs for $\Lambda = 0$, but,…
The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly…
The homogeneous and isotropic radiation dominated universe, following the inflationary stage, is expressed as a spherically symmetric and inhomogeneous spacetime upon a power law type conformal transformation of the null (cosmological)…
We study S-duality transformations that mix the Riemann tensor with the field strength of a 3-form field. The dual of an (A)dS space time - with arbitrary curvature - is seen to be flat Minkowski space time, if the 3-form field has…
The Eddington Lagrangian in the purely affine formulation of general relativity generates the Einstein equations with the cosmological constant. The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, which has the…