On higher dimensional self-similar axion-dilaton solutions

We show that solutions of the self-similar gravitational collapse in the Einstein-axion-dilaton system exist in higher-dimensional spacetimes. These solutions are invariant under spacetime dilation combined with internal SL(2,R) transformations. We rely on the recent setup of Antonelli and Hatefi (JHEP 03:074, arXiv:1912.00078 [hep-th], 2020) and use it for the three different conjugacy classes (elliptic, parabolic and hyperbolic) in higher dimensions. Lastly, we identify new families of physically distinguishable self-similar solutions for all three conjugacy classes in six and seven dimensions.