2015/03/31 by Aghil Alaee, Hari K. Kunduri, Hari K Kunduri
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black hole (networking) #Class (philosophy) #Einstein #Einstein field equations #False vacuum #Geometry and complex manifolds #Interval (graph theory) #Invariant (physics) #Maxima and minima #Nonlinear Partial Differential Equations #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/32/16/165020
published as Class.Quant.Grav. 32 (2015) 16, 165020 · v2. statement of main theorem clarified, various minor improvements and clarifications
openalex publication_date 2015/07/30 · arxiv created 2015/08/12 · arxiv updated 2015/08/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider initial data for extreme vacuum asymptotically flat black holes with R × U ( 1 ) 2 symmetry. Such geometries are critical points of a mass functional defined for a wide class of asymptotically flat, ‘ ( t − ϕ i ) ’ symmetric maximal initial data for the vacuum Einstein equations. We prove that the above extreme geometries are local minima of mass among nearby initial data (with the same interval structure) with fixed angular momenta. Thus the ADM mass of nearby data m ⩾ f ( J 1 , J 2 ) for some function f depending on the interval structure. The proof requires that the initial data of the critical points satisfy certain conditions that are satisfied by the extreme Myers–Perry and extreme black ring data.