Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-02-25
Commun.Math.Phys. 193 (1998) 219-231
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
16 pages LaTeX, uses diagram.sty and auxdefs.sty macros, 2 encapsulated Postscript figures
Scientific paper
10.1007/s002200050326
Working in the Palatini formalism, we describe a procedure for constructing degenerate solutions of general relativity on 4-manifold M from certain solutions of 2-dimensional 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 4-dimensional BF theory. Moreover, there is a correspondence between these solutions and certain solutions of 2-dimensional 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 3-manifold S, at fixed time our solutions typically describe `flux tubes of area': the 3-metric 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.
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