Gustav Holzegel et al 2007 Class. Quantum Grav. 24 6201 doi:10.1088/0264-9381/24/24/004
Gustav Holzegel1, Thomas Schmelzer2 and Claude Warnick1
Show affiliationsWe use the Ricci flow with surgery to study four-dimensional SU(2) × U(1)-symmetric metrics on a manifold with fixed boundary given by a squashed 3-sphere. Depending on the initial metric we show that the flow converges to either the Taub–Bolt or the Taub–NUT metric, the latter case potentially requiring surgery at some point in the evolution. The Ricci flow allows us to explore the Euclidean action landscape within this symmetry class. This work extends the recent work of Headrick and Wiseman (2006 Class. Quantum Grav. 23 6683) to more interesting topologies.
04.20.Gz Spacetime topology, causal structure, spinor structure
02.40.Ky Riemannian geometries
04.20.Ex Initial value problem, existence and uniqueness of solutions
83C75 Space-time singularities, cosmic censorship, etc.
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries
Issue 24 (21 December 2007)
Received 1 August 2007, in final form 26 October 2007
Published 27 November 2007
Gustav Holzegel et al 2007 Class. Quantum Grav. 24 6201
Jürgen Blum et al 1999 Meas. Sci. Technol. 10 836
Nelson Christensen et al 2004 Class. Quantum Grav. 21 S1747
Ting Yu et al 2004 Nanotechnology 15 1732
Stephen C Anco 2002 Class. Quantum Grav. 19 6445
C Lewiner and G Bastard 1980 J. Phys. C: Solid State Phys. 13 2347
Michael Köhl et al 2006 J. Phys. B: At. Mol. Opt. Phys. 39 S47
A N F Aleixo et al 2002 J. Phys. A: Math. Gen. 35 9063
S B Whitfield et al 1994 J. Phys. B: At. Mol. Opt. Phys. 27 L359
George Chavchanidze 2005 J. Phys. A: Math. Gen. 38 6517