arXiv research

Study of 3D vacuum static spaces with specific curvature properties.

The paper classifies vacuum static spaces with harmonic curvature.

Extends static vacuum metrics with specific boundary conditions.

Classifies patterns of symmetry breaking and vacuum degeneracy in scalar and gauge fields.

Proves no-hair theorem for certain vacuum black holes.

Classifies vacuum static spaces with harmonic curvature.

Existence proved for static vacuum extensions near Schwarzschild spheres.

We develop a general method of proving the ellipticity of boundary value problems for the stationary vacuum space time, by showing that the stationary vacuum field equations are elliptic subjected to a geometrically natural collection of boundary conditions in the projection formalism. Using this we prove the manifold …

Match van Stockum dust to vacuum metrics with a single parameter.

Initial data for $pp$-wave spacetimes constructed in 4D.

New static vacuum metrics confirmed for near Euclidean boundary data.

The study finds compact vacuum static spaces with positive isotropic curvature are spheres or products of a circle and sphere.

Proves existence of static vacuum metrics with specific boundary data.

Solves initial boundary value problem for vacuum Einstein equations and proves geometric uniqueness.

Researchers create solutions for naked singularities in Einstein vacuum equations.

The paper studies a new vacuum field equation and its solutions.

The study classifies spaces with specific conformal vector fields.

Study geometric properties of generalized vacuum static spaces.

The paper confirms the existence of 5D regular static vacuum solutions with multiple black holes and Kasner asymptotics.

In a recent paper, the authors established the uniqueness of photon spheres in static vacuum asymptotically flat spacetimes by adapting Bunting and Masood-ul-Alam's proof of static vacuum black hole uniqueness. Here, we establish uniqueness of suitably defined sub-extremal photon spheres in static electro-vacuum asympt…

New exact spherically symmetric vacuum solutions found in Finsler gravity.

New method creates vacuum data at minimal and borderline decay thresholds.

We establish a moduli space $\mathbb E$ of stationary vacuum metrics in a spacetime, and set up a well-defined boundary map $Π$ in $\mathbb E$, assigning a metric class with its Bartnik boundary data. Furthermore, we prove the boundary map $Π$ is Fredholm by showing that the stationary vacuum equations (combined with p…

We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n+1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary compact manifold to an asymptotically Euclidean solution of the constraints on R^n. Fo…

It is proved that the only geodesically complete stationary vacuum solution of the Einstein equations is the empty Minkowski space, or a quotient of it by a discrete group of isometries, generalizing a classical result of Lichnerowicz. In addition, we obtain an apriori bound on the curvature of stationary vacuum soluti…

Vacuum gravity shows black holes can form without collapse.

We give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact manifolds. The condition requires a so-called global supersolution but does not require a global subsolution. As a consequ…

We discuss the invariant classification of vacuum Kundt waves using the Cartan-Karlhede algorithm, and the upper bound on the number of iterations of the Karlhede algorithm to classify the vacuum Kundt waves. By choosing a particular coordinate system we partially construct the canonical coframe used in the classificat…

In this paper we discuss the mechanism of spontaneous symmetry breaking from the point view of vacuum pairs, considered as ground states of a Yang-Mills-Higgs gauge theory. We treat a vacuum as a section in an appropriate bundle that is naturally associated with a minimum of a (general) Higgs potential. Such a vacuum s…

We prove uniqueness of the near-horizon geometries arising from degenerate Kerr black holes within the collection of nearby vacuum near-horizon geometries.

We study solutions to the static vacuum Einstein equations on exterior domains with prescribed metric and mean curvature on the inner boundary. It is proved that for any such boundary data near the standard round boundary data in Euclidean space, there exists a unique AF solution to the static vacuum equations realizin…

New self-similarity for Einstein vacuum equations identified.

New vacuum spacetimes without CMC Cauchy surfaces found.

Classifies solutions to vacuum weighted Einstein equations on pr-waves.

Given asymptotically flat initial data on M^3 for the vacuum Einstein field equation, and given a bounded domain in M, we construct solutions of the vacuum constraint equations which agree with the original data inside the given domain, and are identical to that of a suitable Kerr slice (or identical to a member of som…

New findings on how conformal rescalings affect spacetime metrics.

A large class of vacuum space-times is constructed in dimension 4+1 from hyperboloidal initial data sets which are not small perturbations of empty space data. These space-times are future geodesically complete, smooth up to their future null infinity, and extend as vacuum space-times through their Cauchy horizon. Dime…

One of the central difficulties of settling the $L^2$-bounded curvature conjecture for the Einstein -Vacuum equations is to be able to control the causal structure of spacetimes with such limited regularity. In this paper we show how to circumvent this difficulty by showing that the geometry of null hypersurfaces of En…

Study gluing event horizons of Minkowski and Schwarzschild spacetimes.

We develop a framework for understanding the existence of asymptotically flat solutions to the static vacuum Einstein equations with prescribed boundary data consisting of the induced metric and mean curvature on a 2-sphere. A partial existence result is obtained, giving a partial resolution of a conjecture of Bartnik …

We study the existence and uniqueness of solutions to the static vacuum Einstein equations in bounded domains, satisfying the Bartnik boundary conditions of prescribed metric and mean curvature on the boundary.

In this paper, we study vacuum static spaces with the complete divergence of the Bach tensor and Weyl tensor. First, we prove that the vanishing of complete divergence of the Bach tensor and Weyl tensor implies the harmonicity of the metric, and we present examples in which these conditions do not imply Bach flatness. …

Adapting Israel's proof of static black hole uniqueness, we show that the Schwarzschild spacetime is the only static vacuum asymptotically flat spacetime that possesses a suitably defined photon sphere.

Moitvated in part by [3], in this note we obtain a rigidity result for globally hyperbolic vacuum spacetimes in arbitrary dimension that admit a timelike conformal Killing vector field. Specifically, we show that if M is a Ricci flat, timelike geodesically complete spacetime with compact Cauchy surfaces that admits a t…

The paper proves conditions for compact vacuum static spaces to be isometric to spheres.

Estimates mass of static vacuum metrics with small Bartnik data.

In this paper, the radiation field is defined for solutions to Einstein vacuum equations which are close to Minkowski space-time with spacial dimension $n\geq 4$. The regularity properties and asymptotic behavior of those Einstein vacuum solutions are established at the same time. In particular, the map from Cauchy int…

In a seminal paper of 1917, H. Weyl presented a remarkable reduction of the static axisymmetric vacuum Einstein equations, serving as a relatively straightforward technique to generate and explore new solutions. Weyl's reduction was used by Myers in 1987, and independently by Korotkin-Nicolai in 1994, to construct a ne…