On the first G ₁ stiff fluid spike solution in General Relativity

Using the Geroch transformation we obtain the first example of an exact stiff fluid spike solution to the Einstein field equations in a closed form exhibiting a spacelike G ₁ group of symmetries (i.e., with a single isometry). This new solution is of Petrov type I and exhibits a spike crossing which persists to the past, which allows us to better understand spike crossings in the context of structure formation. (paper)