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Conference Paper

Classical GR as a topological theory with linear constraints


Gielen,  Steffen
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Gielen, S. (2011). Classical GR as a topological theory with linear constraints. Journal of Physics: Conference Series, 314: 012044.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-3122-7
We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints. Our analysis clarifies how the discrete constructions of spin foam models are related to a continuum theory with an action principle that is equivalent to general relativity.