Generalized Robertson-Walker Space-Time Admitting Evolving Null Horizons Related to a Black Hole Event Horizon.

K L Duggal

doi:10.1155/2016/9312525

Abstract

A new technique is used to study a family of time-dependent null horizons, called “Evolving Null Horizons” (ENHs), of generalized Robertson-Walker (GRW) space-time such that the metric 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 . 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.

Highlights

Let (M, g) be a (1 + n)-dimensional space-time manifold whose metric g satisfies the following kinematic condition:∇XU = λ (X + g (X, U) U), (1)where U is a timelike unit vector, ∇ denotes the Levi-Civita connection on M, λ is a function, and X is an arbitrary vector field on M
In this paper we show that there exists a physical model of a family of time-dependent null horizons of generalized Robertson-Walker (GRW) space-time which may evolve into a black hole event horizon
A null hypersurface (H, h, l) of the family F of space-time (M, g) is called an Evolving Null Horizon, briefly denoted by ENH, if (i) H is totally umbilical in M and may include a totally geodesic portion; (ii) all equations of motion hold at H and energy tensor Tij is such that Tbalb is future-causal for any future directed null normal l

Summary

Introduction

Let (M, g) be a (1 + n)-dimensional space-time manifold whose metric g satisfies the following kinematic condition:. The reader will see that the kinematic condition (1) on the space-time metric plays an important role in the induced geometry of null hypersurfaces of M. This is our reason to generate GRW space-time instead of stating it as a definition. International Scholarly Research Notices it is too early to be sure) with the latest LIGO [Laser Interferometer Gravitational-Waves Observatory] experiment (as per Press Release of February 11, 2016) which confirms the presence of gravitational waves produced during the final fraction of a second of the merger of two black holes into a single massive spinning black hole. For information on LIGO via video one may try http://mediaassets.caltech.edu/gwave/

Family of Null Hypersurfaces

Physical Interpretation

Conclusion