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Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory: BTZ solution with torsion

Alberto A. Garcia·Friedrich W. Hehl·Christian Heinicke·Alfredo Macias
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Abstract

In (1+2)-dimensional Poincaré gauge gravity, we start from a Lagrangian depending on torsion and curvature which includes additionally {\em translational} and {\em Lorentzian} Chern-Simons terms. Limiting ourselves to to a specific subcase, the Mielke-Baekler (MB) model, we derive the corresponding field equations (of Einstein-Cartan-Chern-Simons type) and find the general vacuum solution. We determine the properties of this solution, in particular its mass and its angular momentum. For vanishing torsion, we recover the BTZ-solution. We also derive the general conformally flat vacuum solution with torsion. In this framework, we discuss {\em Cartan's} (3-dimensional) {\em spiral staircase} and find that it is not only a special case of our new vacuum solution, but can alternatively be understood as a solution of the 3-dimensional Einstein-Cartan theory with matter of constant pressure and constant torque.

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Alberto A. Garcia, Friedrich W. Hehl, Christian Heinicke, Alfredo Macias. 2003-06-20. Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory: BTZ solution with torsion. https://doi.org/10.1103/physrevd.67.124016

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