We will start with a brief discussion about the role of self-similarity for the Einstein vacuum equations and then will introduce our new class of twisted self-similar solutions. The key defining feature of these new self-similar solutions is that while the homothetic vector field is tangent to the past light cone of the origin of dilation symmetry, it does not coincide with the null generators of this hypersurface and instead "twists" around the light cone.
We will explain how to compute formal power series for these twisted self-similar solutions and discuss some applications.
