Related papers: The Einstein metrics with smooth scri
We investigate the Einstein equation with a positive cosmological constant for $4n+4$-dimensional metrics on bundles over Quaternionic K\"ahler base manifolds whose fibers are 4-dimensional Bianchi IX manifolds. The Einstein equations are…
It is shown that solutions to Einstein's field equations with positive cosmological constant can include non-zero rest-mass fields which coexist with and travel unimpeded across a smooth conformal boundary. This is exemplified by the…
In this work we study the existence of homogeneous Einstein metrics on the total space of homogeneous fibrations such that the fibers are totally geodesic manifolds. We obtain the Ricci curvature of an invariant metric with totally geodesic…
On a given closed connected manifold of dimension two, or greater, we consider the squared $L^2$-norm of the scalar curvature functional over the space of constant volume Riemannian metrics. We prove that its critical points have constant…
We study the question of the integrability of Einstein deformations and relate it to the question of the desingularization of Einstein metrics. Our main application is a negative answer to the long-standing question of whether or not every…
Let $M^n$, $n\ge3$, be a compact differentiable manifold with nonpositive Yamabe invariant $\sigma(M)$. Suppose $g_0$ is a continuous metric with $V(M, g_0)=1$, smooth outside a compact set $\Sigma$, and is in $W^{1,p}_{loc}$ for some…
Using a quasi-spherical approximation of an affine-null metric adapted to an asymptotic Bondi inertial frame, we present high order approximations of the metric functions in terms of the specific angular momentum for a slowly rotating…
The cosmological constant $\Lambda$ used to be a freedom in Einstein's theory of general relativity, where one had a proclivity to set it to zero purely for convenience. The signs of $\Lambda$ or $\Lambda$ being zero would describe…
This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…
We discuss a number of topics in the area of conformally compact Einstein metrics, mostly centered around the global existence question of finding such metrics with an arbitrarily prescribed conformal infinity. The paper is partly a survey…
We present a complete classification of Einstein metrics on the space M = I \times S^3, where I is the interval (0,l) or (0,\infty) or their closures, and we consider separate metric functions f and h (functions of I) for the base and fiber…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
An almost Einstein manifold satisfies equations which are a slight weakening of the Einstein equations; Einstein metrics, Poincare-Einstein metrics, and compactifications of certain Ricci-flat asymptotically locally Euclidean structures are…
In the Bondi-Sachs formulation of General Relativity space-time is foliated via a family of null cones. If these null cones are defined such that their vertices are traced by a regular world-line then the metric tensor has to obey…
On a smooth metric measure spacetime $(M,g,e^{-f} dvol_g)$, we define a weighted Einstein tensor. It is given in terms of the Bakry-\'Emery Ricci tensor as a tensor which is symmetric, divergence-free, concomitant of the metric and the…
Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are…
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
It is an important problem in differential geometry to find non-naturally reductive homogeneous Einstein metrics on homogeneous manifolds. In this paper, we consider this problem for some coset spaces of compact simple Lie groups. A new…
This paper makes a formal study of asymptotically hyperbolic Einstein metrics given, as conformal infinity, a conformal manifold with boundary. The space on which such an Einstein metric exists thus has a finite boundary in addition to the…
It is known that the moduli space of Einstein structures in four dimensions is generally considered to be rigid so that Einstein metrics tend to be isolated modulo diffeomorphisms under infinitesimal Einstein deformations. We examine the…