Axialgravisolitons at infinite corners

Gravitational solitons (gravisolitons) are particular exact solutions of Einstein field equation in vacuum build on a given background solution. Their interpretation is not yet fully clear but they contain many of the physically relevant solutions low $N$-solitons solutions. However, a systematic study and characterization of gravisolitons solution for every $N$ is lacking and their relevance in a theory of quantum gravity is not fully understood. This work aims to investigate and characterize some properties of $N$-axialsoliton solutions such as their asymptotically behaviour and asymptotic symmetries given minimal assumptions on the background metric. We develop an explicit systematic asymptotically expansion for the $N$-axialsoliton solution and we compute the leading order of the asymptotic killing vectors. Moreover, in the perspective to better understand the role of gravisolitons in quantum gravity we make a link, and a one of the first explicit test, to the corner symmetry proposal deriving which subalgebra of the universal corner symmetry algebra is generated by the asymptotic Killing vectors of $N$-axialsoliton solution. In the spirit of the corner proposal, the axialgravisoliton corner symmetry algebra (\textfrak{agcsa}) can be useful for the quantization of the non-asymptotically flat sector of gravity while, in the spirit of IR triangle, new soft theorems and memory effects could emerge.