A Hamiltonian Formulation of Topological Gravity

Details A Hamiltonian Formulation of Topological Gravity A Hamiltonian Formulation of Topological Gravity

1993-11-30

arxiv.org/abs/gr-qc/9311035v1

Class.Quant.Grav.11:989-998,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, Mexico preprint ICN-UNAM-93-13

Scientific paper

10.1088/0264-9381/11/4/015

Topological gravity is the reduction of Einstein's theory to spacetimes with vanishing curvature, but with global degrees of freedom related to the topology of the universe. We present an exact Hamiltonian lattice theory for topological gravity, which admits translations of the lattice sites as a gauge symmetry. There are additional symmetries, not present in Einstein's theory, which kill the local degrees of freedom. We show that these symmetries can be fixed by choosing a gauge where the torsion is equal to zero. In this gauge, the theory describes flat space-times. We propose two methods to advance towards the holy grail of lattice gravity: A Hamiltonian lattice theory for curved space-times, with first-class translation constraints.

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