Table of Contents
ISRN Mathematical Physics
Volume 2014 (2014), Article ID 291790, 10 pages
http://dx.doi.org/10.1155/2014/291790
Research Article

Time-Dependent Evolving Null Horizons of a Dynamical Spacetime

Department of Mathematics and Statistics, University of Windsor, Windsor, ON, Canada N9B 3P4

Received 20 November 2013; Accepted 19 December 2013; Published 22 January 2014

Academic Editors: U. Kulshreshtha and W.-H. Steeb

Copyright © 2014 K. L. Duggal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Totally geodesic null hypersurfaces have been widely used in the study of isolated black holes. In this paper, we introduce a new quasilocal notion of a family of totally umbilical null hypersurfaces called evolving null horizons (ENH) of a dynamical spacetime, satisfied under an appropriate energy condition. We focus on a variety of examples of ENHs and in some cases establish their relation with event and isolated horizons. We also present two specific physical models of an ENH in a black hole spacetime. Beside the examples, for further study we propose two open problems on possible general existence of an ENH in a black hole spacetime and its canonical or unique existence. The results of this paper have ample scope of working on totally umbilical null hypersurfaces of Lorentzian and, in general, semiRiemannian manifolds.