Related papers: Higher dimensional black hole initial data with pr…
An explicit global and unique isometric embedding into hyperbolic 3-space, H^3, of an axi-symmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H^3 of surfaces of revolution having…
In a previous paper, we proved a number of optimal rigidity results for Riemannian manifolds of dimension greater than four whose curvature satisfy an integral pinching. In this article, we use the same integral Bochner technique to extend…
We show that the supersymmetric near horizon black hole geometries of 6-dimensional supergravity coupled to any number of scalar and tensor multiplets are either locally $AdS_3\times \Sigma^3$, where \Sigma^3 is a homology 3-sphere, or…
As argued in arXiv:2104.10172, introducing a non-minimally coupled scalar field, three-dimensional Einstein gravity can be extended by infinite families of theories which admit simple analytic generalizations of the charged BTZ black hole.…
An analytical metric of four-dimensional General Relativity, representing an array of collinear and accelerating black holes, is constructed with the inverse scattering method. The solution can be completely regularised from any conical…
The McVittie metric does not describe a physical black hole in an expanding Universe because the curvature scalar and pressure at its event horizon are infinite. We show that extending this metric to an inhomogeneous scale factor, which…
We construct a static spherically symmetric regular black hole with a Minkowski core, and a degenerate inner horizon with vanishing surface gravity. The spacetime contains a non-extremal outer horizon and exhibits two notable features.…
We consider stationary extreme black hole solutions to the Einstein-Yang-Mills equations in four dimensions, allowing for a negative cosmological constant. We prove that any axisymmetric black hole of this kind possesses a near-horizon…
In this paper, we consider asymptotically flat Riemannnian manifolds $(M^n,g)$ with $C^0$ metric $g$ and $g$ is smooth away from a closed bounded subset $\Sigma$ and the scalar curvature $R_g\ge 0$ on $M\setminus \Sigma$. For given $n\le…
Given any asymptotically flat 3-manifold $(M,g)$ with smooth, non-empty, compact boundary $\Sigma$, the conformal conjecture states that for every $\delta>0$, there exists a metric $g' = u^4 g$, with $u$ a harmonic function, such that the…
As shown by Gromov-Lawson and Stolz the only obstruction to the existence of positive scalar curvature metrics on closed simply connected manifolds in dimensions at least five appears on spin manifolds and is given by the non-vanishing of…
Let $M$ be a compact connected oriented $n-1$ dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from $M$ to $\mathbb R^n$. The results of \cite{Michor118}, where mean curvature…
The main result is that every complete finite area hyperbolic metric on a sphere with punctures can be uniquely realized as the induced metric on the surface of a convex ideal polyhedron in hyperbolic 3-space. A number of other observations…
We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous manifold with a 4-dimensional isometry group. The condition is expressed in terms of…
In this work, we study various properties of embedded hypersurfaces in $1+1+2$ decomposed spacetimes with a preferred spatial direction, denoted $e^{\mu}$, which are orthogonal to the fluid flow velocity of the spacetime and admit a proper…
In this work, we investigate the $n$-dimensional charged static black hole solutions in the Einstein-\ae ther theory. By taking the metric parameter $k$ to be $1,0$, and $-1$, we obtain the spherical, planar, and hyperbolic spacetimes…
We establish mean curvature estimate for immersed hypersurface with nonnegative extrinsic scalar curvature in Riemannian manifold $(N^{n+1}, \bar g)$ through regularity study of a degenerate fully nonlinear curvature equation in general…
The near horizon geometry of extremal rotating black hole in arbitrary dimension possesses SO(2,1)xU(n) symmetry in the special case that all n rotation parameters are equal. We consider a conformal particle associated with such a maximally…
A new class of vacuum black holes for the most general gravity theory leading to second order field equations in the metric in even dimensions is presented. These space-times are locally AdS in the asymptotic region, and are characterized…
Consider a one-parameter family of smooth Riemannian metrics on a two-sphere, $\mathscr{S}$. By choosing a one-parameter family of smooth lapse and shift, these Riemannian two-spheres can always be assembled into smooth Riemannian…