arXiv subjects

M. Dunajski

Publications and source records attributed to M. Dunajski.

3 recordsLinked to original sources

arXiv2011

Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Beyond Self-Duality

We construct new supersymmetric solutions to the Euclidean Einstein-Maxwell theory with a non-vanishing cosmological constant, and for which the Maxwell field strength is neither self-dual or anti-self-dual. We find that there are three classes of solutions, depending on the sign of the Maxwell field strength and cosmological constant terms in the Einstein equations which arise from the integrability conditions of the Killing spinor equation. The first class is a Euclidean version of a Lorentzian supersymmetric solution found in arXiv:0804.0009, hep-th/0406238 . The second class is constructed from a three dimensional base space which admits a hyper-CR Einstein-Weyl structure. The third class is the Euclidean Kastor-Traschen solution.

hep-th↗

arXiv2004

Solitons and admissible families of rational curves in twistor spaces

It is well known that twistor constructions can be used to analyse and to obtain solutions to a wide class of integrable systems. In this article we express the standard twistor constructions in terms of the concept of an admissible family of rational curves in certain twistor spaces. Examples of of such families can be obtained as subfamilies of a simple family of rational curves using standard operations of algebraic geometry. By examination of several examples, we give evidence that this construction is the basis of the construction of many of the most important solitonic and algebraic solutions to various integrable differential equations of mathematical physics. This is presented as evidence for a principal that, in some sense, all soliton-like solutions should be constructable in this way.

math-ph↗

arXiv1998

From 2D Integrable Systems to Self-Dual Gravity

We explain how to construct solutions to the self-dual Einstein vacuum equations from solutions of various two-dimensional integrable systems by exploiting the fact that the Lax formulations of both systems can be embedded in that of the self-dual Yang--Mills equations. We illustrate this by constructing explicit self-dual vacuum metrics on $\R^2\times Σ$, where $Σ$ is a homogeneous space for a real subgroup of $SL(2, \C)$ associated with the two-dimensional system.

solv-int↗