Explicit self-similar solutions of time-like extremal hypersurfaces in ${\mathbb{R}}^{1+3}$

Abstract

In this letter, two explicit self-similar solutions to a graph representation of time-like extremal hypersurfaces in Minkowski spacetime ${\mathbb{R}}^{1+3}$ are given. Meanwhile, there is an untable eigenvalue in the linearized time-like extremal hypersurfaces equation around two explicit self-similar solutions.

5page, correct some English errors, and add four references. This letter is one of parts in our paper [12]

References in corpus (1)

• On smoothness of timelike maximal cylinders in three dimensional vacuum spacetimes