Mathematics – General Topology
Scientific paper
May 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009aipc.1122..115b&link_type=abstract
PHYSICS AND MATHEMATICS OF GRAVITATION: Proceedings of the Spanish Relativity Meeting 2008. AIP Conference Proceedings, Volume
Mathematics
General Topology
General Topology, Kaluza-Klein Theories, Supergravity
Scientific paper
In the Kaluza-Klein framework of gravity theories one has extra dimensions in the form of small, compact manifolds. The form and the dynamics of these manifolds can have significant impact on the external geometry, for example their topology is related to the number of light degrees of freedom as seen in the low energy theory. So, if the geometry is able to change, then the low energy theory sees a change in the low energy degrees of freedom; this would manifest itself as a phase transition. In this note we examine the role of gravity as such a topology change is attempted. We start by considering the evolution of an Eguchi-Hanson geometry by allowing the minimal 2-cycle to contract, including all the relevant gravitational degrees of freedom, finding that the two cycle either halts its collapse, followed by it expanding, or a black hole is formed. We comment on the type of black that is formed. We also consider the case of the collapse of a smooth conifold-both resolved and deformed.
Butcher Neil A.
Saffin Paul M.
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