Some 3-dimensional maximally symmetric solutions of Einstein-aether theory

摘要

Working in isotropic coordinates, we get some maximally symmetric nonrotating solutions of the Einstein-aether theory in 2 + 1 dimensions, all in analytical forms. Curvature singularities are not found in the Ricci and Kretschmann scalars, while conical singularities are avoidable by fixing some integration constants. In Schwarzschild type coordinates, most line elements become the metric of a black hole or a massive particle in the 2 + 1-dimensional de Sitter or anti-de Sitter space-time, but in some solutions the aether field cannot be written in closed forms.

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