Related papers: Gravitational instantons with faster than quadrati…
In this paper, we study gravitational instantons (i.e., complete hyperk\"aler 4-manifolds with faster than quadratic curvature decay). We prove three main theorems: 1.Any gravitational instanton must have known end----ALE, ALF, ALG or ALH.…
This is our third paper in a series on the gravitational instantons. In this paper, we classify ALG and ALH gravitational instantons. In ALG case, we extend Hein's construction slightly and show that it's the only ALG gravitational…
We obtain $D_k$ ALF gravitational instantons by a gluing construction which captures, in a precise and explicit fashion, their interpretation as non-linear superpositions of the moduli space of centred $SU(2)$ monopoles, equipped with the…
There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type ALG and ALG$^*$. Gravitational instantons of type ALG were previously classified by Chen-Chen. In this paper, we prove a…
We prove the instability of conformally K\"ahler, compact or ALF Einstein 4-manifolds with nonnegative scalar curvature which are not half conformally flat. This applies to all the known examples of gravitational instantons which are not…
A classification result for Ricci-flat anti-self-dual asymptotically locally Euclidean 4-manifolds is obtained: they are either hyperk\"ahler (one of the gravitational instantons classified by Kronheimer), or they are a cyclic quotient of a…
We describe a quaternionic-based Ansatz generalizing the Gibbons-Hawking Ansatz to a class of hyperk\"ahler metrics with hidden symmetries. We then apply it to obtain explicit expressions for gravitational instanton metrics of type $D_k$.
This paper is the sequel of our previous article "From ALE to ALF gravitational instantons", where we constructed ALF hyperkahler metrics on minimal resolutions of dihedral Kleinian singularities. In the present article we generalize the…
This is a review of gravitational instantons -- solutions to Riemannian Einstein or Einstein-Maxwell equations in four dimensions which yield complete metrics on non-compact four-manifolds, and which asymptotically `look like' flat space.…
We use two different methods to obtain Asymptotically Locally Flat hyperkahler metrics of type D_k.
It has long been conjectured that the Euclidean Schwarzschild and Euclidean Kerr instantons are the only non-trivial asymptotically flat (AF) gravitational instantons. In this letter, we show that this conjecture is false by explicitly…
We give a simple and uniform construction of essentially all known deformation classes of gravitational instantons with ALF, ALG or ALH asymptotics and nonzero injectivity radius. We also construct new ALH Ricci flat metrics asymptotic to…
We construct the explicit form of three almost complex structures that a Riemannian manifold with self-dual curvature admits and show that their Nijenhuis tensors vanish so that they are integrable. This proves that gravitational instantons…
We classify all scalar-flat toric K\"ahler 4-manifolds under either of two asymptotic conditions: that the action fields decay slowly (or at all), or that the curvature decay is quadratic; for example we fully classify instantons that have…
We show that every gravitational instantons are SU(2) Yang-Mills instantons on a Ricci-flat four manifold although the reverse is not necessarily true. It is shown that gravitational instantons satisfy exactly the same self-duality equation…
In this paper we propose ALF gravitational instantons of types A_k and D_k as models for charged particle systems. We calculate the charges of the two families. These are -(k +1) for A_k, which is proposed as a model for k+1 electrons, and…
In this paper, we construct families of gravitational instantons of type ALG, ALG*, ALH and ALH* using a gluing construction. Away from a finite set of exceptional points, the metric collapses with bounded curvature to a quotient of…
A new two-parameter asymptotically flat (AF) toric gravitational instanton is identified as a special case of the Euclidean double Kerr-NUT solution, by imposing certain symmetry and regularity conditions on its rod structure. These…
We construct large families of new collapsing hyperk\"ahler metrics on the K3 surface. The limit space is the quotient of a flat 3-torus by an involution. Away from finitely many exceptional points the collapse occurs with bounded…
An instanton $(E, D)$ on a (pseudo-)hyperk\"ahler manifold $M$ is a vector bundle $E$ associated to a principal $G$-bundle with a connection $D$ whose curvature is pointwise invariant under the quaternionic structures of $T_x M, \ x\in M$,…