Null hypersurfaces evolved by their mean curvature in a Lorentzian manifold
Volume 157 / 2019
Colloquium Mathematicum 157 (2019), 83-106
MSC: Primary 53C50; Secondary 53C44, 53C40.
DOI: 10.4064/cm7450-8-2018
Published online: 1 March 2019
Abstract
We use null isometric immersions to introduce time-dependent null hypersurfaces, in a Lorentzian manifold, evolving in the direction of their mean curvature vector (a vector transversal to the null hypersurface). We prove an existence result for such hypersurfaces in a short-time interval. Then, we discuss the evolution of some induced geometric objects. Consequently, we prove under certain geometric conditions that some of the above objects will blow-up in finite time. Also, several examples are given to illustrate the main ideas.
