6 papers
On toric self-dual Einstein gravitational instantons
Bernardo Araneda, James Lucietti, Virinchi Rallabhandi
We consider the classification of toric self-dual Einstein gravitational instantons with negative cosmological constant. As is well known, any Killing vector field on a self-dual E…
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…
On the existence of toric ALE and ALF gravitational instantons
Hari K. Kunduri, James Lucietti
We establish existence and uniqueness results for asymptotically locally Euclidean (ALE) and asymptotically locally flat (ALF) gravitational instantons. In particular, we prove the…
All toric Hermitian ALE gravitational instantons
Bernardo Araneda, James Lucietti
We prove that the only smooth, Ricci flat, ALE instanton with a toric Hermitian non-Kähler structure is the Eguchi-Hanson instanton. The proof is analogous to the classification o…
Intrinsic rigidity of extremal horizons
Maciej Dunajski, James Lucietti
We prove that the intrinsic geometry of compact cross-sections of any vacuum extremal horizon must admit a Killing vector field. If the cross-sections are two-dimensional spheres,…
Rigidity of the extremal Kerr-Newman horizon
Alex Colling, David Katona, James Lucietti
We prove that the intrinsic geometry of compact cross-sections of an extremal horizon in four-dimensional Einstein-Maxwell theory must admit a Killing vector field or is static. Th…