相关论文: Einstein Metrics on Spheres

In Einstein-scalar-Maxwell theories with a coupling between the scalar field $\phi$ and the electromagnetic field strength $F$ of the form $\mu(\phi) F$, we investigate the existence of exotic compact objects (ECOs) and their observational…

The exact static spherically symmetric solutions for pure-aether theory and Einstein-aether theory are presented. It is shown that both theories can deliver the Schwarzschild metric, but only the Einstein-aether theory contains solutions…

We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills…

Using the twistor correspondence, we give a classification of toric anti-self-dual Einstein metrics: each such metric is essentially determined by an odd holomorphic function. This explains how the Einstein metrics fit into the…

In this paper, we study the coupled Einstein constraint equations on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. This is physically well-motivated by standard cosmological…

We study the observability of waves on gas giant manifolds which are a class of Riemannian manifolds whose metrics are singular at the boundary. Such manifolds arise naturally in modeling of acoustic wave propagation in gas giant planets.We…

Shape metrics for objects in high dimensions remain sparse. Those that do exist, such as hyper-volume, remain limited to objects that are better understood such as Platonic solids and $n$-Cubes. Further, understanding objects of ill-defined…

Let $ M = G/K $ be a full flag manifold. In this work, we investigate the $ G$-stability of Einstein metrics on $M$ and analyze their stability types, including coindices, for several cases. We specifically focus on $F(n) =…

We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…

We present a construction of complete self-dual Einstein metrics of negative scalar curvature on an uncountable family of manifolds of infinite topological type, which are enumerated by continued fraction expansions of irrational numbers.…

The invariant metric affine connections on Berger spheres which are Einstein with skew torsion are determined in both Riemannian and Lorentzian signature. Expressions of such connections are explicitly given. In particular, every Berger…

The usual description of 2+1 dimensional Einstein gravity as a Chern-Simons (CS) theory is extended to a one parameter family of descriptions of 2+1 Einstein gravity. This is done by replacing the Poincare' gauge group symmetry by a…

We give estimates on the length of paths defined in the sphere model of outer space using a surgery process, and show that they make definite progress in some sense when they remain in some thick part of outer space. To do so, we relate the…

The Einstein-Cartan equations in first-order action of torsion are considered. From Belinfante-Rosenfeld equation special consistence conditions are derived for the torsion parameters relating them to the metric. Inside matter the torsion…

This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…

Starting with a compact hyperbolic cone-manifold of dimension n > 2, we study the deformations of the metric in order to get Einstein cone-manifolds. If the singular locus is a closed codimension 2 submanifold and all cone angles are…

The famous theorems of Cartan, related to the axiom of $r$-planes, and Leung-Nomizu about the axiom of $r$-spheres were extended to K\"ahler geometry by several authors. In this paper we replace the strong notions of totally geodesic…

A four dimensional pseudo-Riemannian manifold of signature (2, 2) is called a Walker manifold if it admits a parallel degenerate plane field. In this paper, we study the curvature properties of such a class of four dimensional Walker…

In this paper we study the problem of prescribing a fourth order conformal invariant (the Paneitz curvature) on the $n$-sphere, with $n\geq 5$. Using tools from the theory of critical points at infinity, we provide some topological…

Various curvature conditions are studied on metrics admitting a symmetry group. We begin by examining a method of diagonalizing cohomogeneity-one Einstein manifolds and determine when this method can and cannot be used. Examples, including…