Gravitational collapse of cylindrical anisotropic fluid: a source of gravitational waves

Abstract

The present work deals with dynamics of gravitational collapse with cylindrical symmetry as developed by Misner and Sharp. The interior collapsing anisotropic cylindrical perfect fluid is matched to an exterior vacuum cylindrically symmetric space-time due to Einstein-Rosen using the Darmois matching conditions. It is found that the radial pressure of the anisotropic perfect fluid is non-zero on the boundary surface and is related to the components of shear viscosity. As a result, there is formation of gravitational waves outside the collapsing matter.

Static and Dynamic Melvin Universes

“…We relax the conformal collapse condition in Appendix C and consider, for instance, the collapse of the whole horizontal space of the Melvin magnetic universe around the axis of cylindrical symmetry. Cylindrical gravitational collapse has been discussed in general relativity by a number of authors, see [35][36][37][38][39][40] and the references cited therein. These investigations involved, for the most part, collapsing cylindrical systems that were matched to exterior vacuum Einstein-Rosen spacetimes in order to study the cylindrical gravitational radiation generated via gravitational collapse.…”

“…where ω, µ and k z are constants. The wave function Φ representing a neutral scalar field is real and satisfies a linear wave equation; for the sake of simplicity, Φ can be written in complex form (40) with the convention that its real part has physical significance. The background static configuration is invariant under φ → φ + 2π; therefore, we conclude that µ = n = 0, ±1, ±2, ±3, • • • .…”

A Study of Charged Cylindrical Gravitational Collapse with Dissipative Fluid

“…Further, cylindrical collapse of nondissipative fluid with exterior containing gravitational waves shows nonvanishing pressure on the boundary surface by using Darmois matching conditions. Recently, it has been verified [25,26] in studying cylindrical collapse of anisotropic dissipative fluid with formation of gravitational waves outside the collapsing matter.…”