2003/01/31 by M. M. Akbar, M.M Akbar
Mathematics · Physics and Astronomy · #Anti-de Sitter space #Black Holes and Theoretical Physics #Boundary (topology) #Constant (computer programming) #Cosmological constant #De Sitter universe #Geometric Analysis and Curvature Flows #Gravitation #Isotropy #Limit (mathematics) #Noncommutative and Quantum Gravity Theories #Quantum gravity #gr-qc #hep-th
paper · pdf · doi:10.1016/s0550-3213(03)00376-6
published as Nucl.Phys. B663 (2003) 215-230 · Minor changes and references added: Version in the Journal
openalex publication_date 2003/05/27 · arxiv created 2003/08/26 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
For an SU(2)× U(1)-invariant S3 boundary the classical Dirichlet problem of Riemannian quantum gravity is studied for positive-definite regular solutions of the Einstein equations with a negative cosmological constant within biaxial Bianchi-IX metrics containing bolts, i.e., within the family of Taub-Bolt-anti-de Sitter (Taub-Bolt-AdS) metrics. Such metrics are obtained from the two-parameter Taub-NUT-anti-de Sitter family. The condition of regularity requires them to have only one free parameter (L) and constrains L to take values within a narrow range; the other parameter is determined as a double-valued function of L and hence there is a bifurcation within the family. We found that \itany axially symmetric S3-boundary can be filled in with at least one solution coming from each of these two branches despite the severe limit on the permissible values of L. The number of infilling solutions can be one, three or five and they appear or disappear catastrophically in pairs as the values of the two radii of S3 are varied. The solutions occur simultaneously in both branches and hence the total number of independent infillings is two, six or ten. We further showed that when the two radii are of the same order and large the number of solutions is two. In the isotropic limit this holds for small radii as well. These results are to be contrasted with the one-parameter self-dual Taub-NUT-AdS infilling solutions of the same boundary-value problem studied previously.