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Actions for Gravity, with Generalizations: A Review

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arxiv gr-qc/9305011 v1 pith:CB57UZ33 submitted 1993-05-13 gr-qc

Peter Peldan This is my paper · ORCID
classification gr-qc
keywords gravitydimensionsactionsgeneralizationsreviewthereashtekarclassical
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Related to the classical Ashtekar Hamiltonian, there have been discoveries regarding new classical actions for gravity in (2+1)- and (3+1)-dimensions, and also generalizations of Einstein's theory of gravity. In this review, I will try to clarify the relations between the new and old actions for gravity, and also give a short introduction to the new generalizations. The new results/treatments in this review are: 1. A more detailed constraint analysis of the Hamiltonian formulation of the Hilbert- Palatini Lagrangian in (3+1)-dimensions. 2. The canonical transformation relating the Ashtekar- and the ADM-Hamiltonian in (2+1)-dimensions is given. 3. There is a discussion regarding the possibility of finding a higher dimensional Ashtekar formulation. There are also two clarifying figures (in the beginning of chapter 2 and 3, respectively) showing the relations between different action-formulations for Einstein gravity in (2+1)- and (3+1)-dimensions.

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Cited by 2 Pith papers

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  1. Generators of Local Lorentz Transformation in ADM-Vielbein Formalism of Gravitational Relativity

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    In the tetrad (ADM-vielbein) form of general relativity, the authors build first-class constraints that generate the full local Lorentz group (rotations plus boosts) and verify the Lorentz algebra, but only for N=1, Ni=0.

  2. Different types of torsion and their effect on the dynamics of fields

    gr-qc 2019-07 unverdicted novelty 5.0 of 10

    In VEP formalism the off-shell spin connection admits a one-parameter family of conformal transformations interpolating between Nieh-Yan and conformally invariant torsion; dynamically generated torsion lacks well-defi...

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