Poincaré gauge theory of gravity

Abstract

A Poincaré gauge theory of (2+1)-dimensional gravity is developed. Fundamental gravitational field variables are dreibein fields and Lorentz gauge potentials, and the theory is underlain with the Riemann-Cartan space-time. The most general gravitational Lagrangian density, which is at most quadratic in curvature and torsion tensors and invariant under local Lorentz transformations and under general coordinate transformations, is given. Gravitational field equations are studied in detail, and solutions of the equations for weak gravitational fields are examined for the case with a static, \lq \lq spin"less point like source. We find, among other things, the following: (1)Solutions of the vacuum Einstein equation satisfy gravitational field equations in the vacuum in this theory. (2)For a class of the parameters in the gravitational Lagrangian density, the torsion is \lq \lq frozen" at the place where \lq \lq spin" density of the source field is not vanishing. In this case, the field equation actually agrees with the Einstein equation, when the source field is \lq \lq spin"less. (3)A teleparallel theory developed in a previous paper is \lq \lq included as a solution" in a limiting case. (4)A Newtonian limit is obtainable, if the parameters in the Lagrangian density satisfy certain conditions.

27pages, RevTeX, OCU-PHYS-152

References in corpus (3)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Closed time like curve and the energy condition in 2+1 dimensional gravity

Cited by in corpus (21)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory: BTZ solution with torsion
• Reissner-Nordström Spacetime in the Tetrad Theory of Gravitation
• Charged Axially Symmetric Solution and Energy in Teleparallel Theory Equivalent to General Relativity
• Energy-momentum current for coframe gravity
• Black hole entropy in 3D gravity with torsion
• New solutions in 3D gravity
• Conserved currents in gravitational models with quasi-invariant Lagrangians: Application to teleparallel gravity
• Asymptotic symmetries in 3d gravity with torsion
• Gauge field theory for Poincaré-Weyl group
• Dirac quasinormal modes of Chern-Simons and BTZ black holes with torsion
• Asymptotic dynamics in 3D gravity with torsion
• Energy of spherically symmetric spacetimes on regularizing teleparallelism
• Covariant description of the black hole entropy in 3D gravity
• On a class of invariant coframe operators with application to gravity
• Energy and angular momentum of general 4-dimensional stationary axi-symmetric spacetime in teleparallel geometry
• Interaction of the 4-rotational gauge field with orbital momentum, gravidiamagnetic effect, and orbit experiment "Gravity Probe B"
• On the geometric foundation of classical gauge gravitation theory
• A class of quasi-linear equations in coframe gravity
• Energy, momentum and angular momentum conservations in de Sitter gravity
• de Sitter-covariant Hamiltonian formalism of Einstein--Cartan gravity