7 papers
Quasi-Einstein structures and Hitchin's equations
Alex Colling, Maciej Dunajski
We prove (Theorem 1.1.) that a class of quasi-Einstein structures on closed manifolds must admit a Killing vector field. This extends the rigidity theorem obtained in \cite{DL23} f…
Near--extremal gravitational collapse in 4+1 dimensions: Schwarzschild--de--Sitter space
Maciej Dunajski, Sebastian J. Szybka
We numerically study a formation of near extremal horizons from a gravitational collapse of radially symmetric gravitational waves in dimensions within the framework of pure…
New quasi-Einstein metrics on a two-sphere
Alex Colling, Maciej Dunajski, Hari Kunduri +1
We construct all axi-symmetric non-gradient -quasi-Einstein structures on a two-sphere. This includes the spatial cross-section of the extreme Kerr black hole horizon correspond…
Integrable Systems
Maciej Dunajski
These notes are based on lecture courses I gave to third year mathematics students at Cambridge. They could form a basis of an elementary one--term lecture course on integrable sys…
New asymptotically flat Einstein--Maxwell instantons
Bernardo Araneda, Maciej Dunajski
We disprove the Euclidean Einstein--Maxwell Black Hole Uniqueness Conjecture, and thus demonstrate that the semi-classical properties of coupled gravitational and electromagnetic f…
Conformally Kähler structures
Maciej Dunajski, A. Rod Gover
We establish a one-to-one correspondence between Kähler metrics in a given conformal class and parallel sections of a certain vector bundle with conformally invariant connection,…