Generalized Robertson-Walker space-time admitting evolving null horizons related to a black hole event horizon (Q1727805)

Summary: A new technique is used to study a family of time-dependent null horizons, called ``\textit{Evolving Null Horizons}'' (ENHs), of generalized Robertson-Walker (GRW) space-time \((\overline{M}, \overline{g})\) such that the metric \(\overline{g}\) satisfies a kinematic condition. This work is different from our early papers on the same issue where we used \((1 + n)\)-splitting space-time but only some special subcases of GRW space-time have this formalism. Also, in contrast to previous work, we have proved that each member of ENHs is totally umbilical in \((\overline{M}, \overline{g})\). Finally, we show that there exists an ENH which is always a null horizon evolving into a black hole event horizon and suggest some open problems.