English

Actions for Gravity, with Generalizations: A Review

General Relativity and Quantum Cosmology 2010-04-06 v1

Abstract

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.

Keywords

Cite

@article{arxiv.gr-qc/9305011,
  title  = {Actions for Gravity, with Generalizations: A Review},
  author = {Peter Peldan},
  journal= {arXiv preprint arXiv:gr-qc/9305011},
  year   = {2010}
}

Comments

61 pages, ITP 93-13

R2 v1 2026-07-22T12:48:21.616Z