Abstract

The existence of special solutions is investigated for Poincare gauge theory with linear and quadratic Lagrangians. A method is used which is similar to the one employed by Yasskin for Yang-Mills-type gauge theories. The investigation is first done for a Lorentz gauge field in vacuum which is not accompanied by a translational gauge field. It is then shown that there are two series of special solutions which can be generated by a massive (or a massless) vector field. A similar investigation is also made for a Lorentz gauge field accompanied by a translational gauge field. Then equations are obtained which can be looked upon as the Einstein-Maxwell equations. This situation is quite similar to the one in Yang-Mills-type gauge theories.

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