Related papers: The Einstein metrics with smooth scri
It has been observed by Maldacena that one can extract asymptotically anti-de Sitter Einstein $4$-metrics from Bach-flat spacetimes by imposing simple principles and data choices. We cast this problem in a conformally compact Riemannian…
We prove dynamical stability and instability theorems for compact Einstein metrics under the Ricci flow. We give a nearly complete charactarization of dynamical stability and instability in terms of the conformal Yamabe invariant and the…
We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kahler metrics with constant scalar curvature, and metrics with harmonic curvature. With…
We introduce a systematic method to produce left-invariant, non-Ricci-flat Einstein metrics of indefinite signature on nice nilpotent Lie groups. On a nice nilpotent Lie group, we give a simple algebraic characterization of non-Ricci-flat…
We prove the existence of Sasakian-Einstein metrics on infinitely many rational homology spheres in all odd dimensions greater than 3. In dimension 5 we obain somewhat sharper results. There are examples where the number of effective…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor…
We explore singularity-free and geodesically-complete cosmologies based on manifolds that are not quite Lorentzian. The metric can be either smooth everywhere or non-degenerate everywhere, but not both, depending on the coordinate system.…
In the famous textbook written by Landau and Lifshitz all the vacuum metrics of the general theory of relativity are derived, which depend on one coordinate in the absence of a cosmological constant. Unfortunately, when considering these…
We discuss the linearization of Einstein equations in the presence of a cosmological constant, by expanding the solution for the metric around a flat Minkowski space-time. We demonstrate that one can find consistent solutions to the…
We survey some aspects of the current state of research on Einstein metrics on compact 4-manifolds. A number of open problems are presented and discussed.
The Einstein-Schrodinger theory is modified by adding a cosmological constant contribution caused by zero-point fluctuations. This cosmological constant which multiplies the symmetric metric is assumed to be nearly cancelled by…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
Let $M = G/H$ be a connected simply connected homogeneous manifold of a compact, not necessarily connected Lie group $G$. We will assume that the isotropy $H$-module $\mathfrak {g/h}$ has a simple spectrum, i.e. irreducible submodules are…
The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial…
In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions on a Kahler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets…
The Schwarzschild-deSitter metric is the known solution of Einstein field equations with cosmological constant term for vacuum spherically symmetric space around a point mass M. Recently it has been reported that in a $Lamda$-dominant world…
We discuss simple vacuum solutions to the Einstein Equations in five dimensional space-times compactified in two different ways. In such spaces, one black hole phase and more then one black string phase may exist. Several old metrics are…
In this article, we achieved several non-naturally reductive Einstein metrics on exceptional simple Lie groups, which are formed by the decomposition arising from general Wallach spaces. By using the decomposition corresponding to the two…
We investigate five dimensional Einstein spaces in warped geometries from the point of view of the four dimensional physically relevant Robertson-Walker-Friedman cosmological metric and the Schwarzschild metric. We show that a…