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arXiv · 1704.07391

New boundary variables for classical and quantum gravity on a null surface

Wolfgang Wieland
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Abstract

The covariant Hamiltonian formulation for general relativity is studied in terms of self-dual variables on a manifold with an internal and lightlike boundary. At this inner boundary, new canonical variables appear: a spinor and a spinor-valued two-form that encode the entire intrinsic geometry of the null surface. At a two-dimensional cross-section of the boundary, quasi-local expressions for the generators of two-dimensional diffeomorphisms, time translations, and dilatations of the null normal are introduced and written in terms of the new boundary variables. In addition, a generalisation of the first-law of black-hole thermodynamics for arbitrary null surfaces is found, and the relevance of the framework for non-perturbative quantum gravity is stressed and explained.

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Wolfgang Wieland. 2017-04-24. New boundary variables for classical and quantum gravity on a null surface. https://doi.org/10.1088/1361-6382%2Faa8d06

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