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Degenerate Solutions of General Relativity from Topological Field Theory  John C. Baez
;  Date: 
25 Feb 1997  Journal:  Commun.Math.Phys. 193 (1998) 219231  Subject:  General Relativity and Quantum Cosmology; Quantum Algebra  grqc hepth math.QA qalg  Abstract:  Working in the Palatini formalism, we describe a procedure for constructing degenerate solutions of general relativity on 4manifold M from certain solutions of 2dimensional BF theory on any framed surface Sigma embedded in M. In these solutions the cotetrad field e (and thus the metric) vanishes outside a neighborhood of Sigma, while inside this neighborhood the connection A and the field E = e ^ e satisfy the equations of 4dimensional BF theory. Moreover, there is a correspondence between these solutions and certain solutions of 2dimensional BF theory on Sigma. Our construction works in any signature and with any value of the cosmological constant. If M = R x S for some 3manifold S, at fixed time our solutions typically describe `flux tubes of area’: the 3metric vanishes outside a collection of thickened links embedded in S, while inside these thickened links it is nondegenerate only in the two transverse directions. We comment on the quantization of the theory of solutions of this form and its relation to the loop representation of quantum gravity.  Source:  arXiv, grqc/9702051  Services:  Forum  Review  PDF  Favorites 


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