2021/07/31 by Hari K. Kunduri, James Lucietti · 6 citations
Mathematics · Physics and Astronomy · #gr-qc #hep-th #math-ph #math.DG #math.MP
paper · pdf · doi:10.1007/s11005-021-01475-1
published as Lett Math Phys 111, 133 (2021) · 29 pages, 3 figures. v2: remark on static case added, references added. v3: minor clarifications, published version. v4: minor correction and clarification in Introduction and Section 2.3, updated since published version (results unchanged)
arxiv created 2022/04/12 · arxiv updated 2022/04/13
We prove uniqueness and existence theorems for four-dimensional asymptotically flat, Ricci-flat, gravitational instantons with a torus symmetry. In particular, we prove that such instantons are uniquely characterised by their rod structure, which is data that encodes the fixed point sets of the torus action. Furthermore, we establish that for every admissible rod structure there exists an instanton that is smooth up to possible conical singularities at the axes of symmetry. The proofs involve adapting the methods that are used to establish black hole uniqueness theorems, to a harmonic map formulation of Ricci-flat metrics with torus symmetry, where the target space is directly related to the metric (rather than auxiliary potentials). We also give an elementary proof of the nonexistence of asymptotically flat toric half-flat instantons. Finally, we derive a general set of identities that relate asymptotic invariants such as the mass to the rod structure.