Absence of trapped surfaces and singularities in cylindrical collapse

Abstract

The gravitational collapse of an infinite cylindrical thin shell of generic matter in an otherwise empty spacetime is considered. We show that geometries admitting two hypersurface orthogonal Killing vectors cannot contain trapped surfaces in the vacuum portion of spacetime causally available to geodesic timelike observers. At asymptotic future null infinity, however, congruences of outgoing radial null geodesics become marginally trapped, due to convergence induced by shear caused by the interaction of a transverse wave component with the geodesics. The matter shell itself is shown to be always free of trapped surfaces, for this class of geometries. Finally, two simplified matter models are analytically examined. For one model, the weak energy condition is shown to be a necessary condition for collapse to halt; for the second case, it is a sufficient condition for collapse to be able to halt.

Static fluid cylinders and their fields: global solutions

“…We begin with the construction of solutions with a regular axis. Inserting Taylor series for the metric coefficients into the field equations indicates that for a given 4 We choose the pressure rather than the energy density as the fundamental variable since in section 6 we analyze cylinders of incompressible fluids.…”

“…Recently, attention has been mainly paid to dynamical situations or quantum issues. Some of these aspects are surveyed in [1] (section 9 and references [247][248][249][250][251][252][253][254][255][256][257][258][259][260][261][262][263], [275][276][277] therein), for example; for even more recent works, see, e.g., [2,3,4].…”

Effect of radiative gravitational modes on the dynamics of a cylindrical shell of counterrotating particles

“…Equation (2) is the integrability condition of Eqs. (3). The coordinates (z, φ, r) and the metric function ψ are continuous across the shell Σ, while t and the metric function γ are discontinuous.…”

“…The dynamics of these systems was analyzed originally by Apostolatos and Thorne [1], but the evolution was considered in detail only over very short periods of time, and imposing a particular form for the initial data, the "momentarily static radiation free" (MSRF) form [2], and the question of the general evolution in time of the system has remained largely unexplored. We notice that most of the literature that followed the work Apostolatos and Thorne has concentrated in the problem of collapse (see, for instance, [3] and [4]), and in general imposing particular forms for the fields, that may include also some form of non gravitational radiation outside the shell (see, for instance, [5], [6] or [7]). In a recent paper Hamity, Barraco and Cécere [8], have considered again the relativistic dynamics of these systems.…”

Unpolarized radiative cylindrical spacetimes: trapped surfaces and quasilocal energy

“…Cylindrically symmetric spacetimes are the simplest spacetimes with a non-trivial field content which admit exact solutions containing gravitational radiation [1]. They also provide useful test beds for quantum gravity [2], numerical relativity [3], and probes of the hoop and cosmic censorship conjectures [4,5,6]. The best studied vacuum case is that of the Einstein-Rosen (ER) metric [7], which contains two spacelike, commuting, hypersurface-orthogonal Killing vector fields, ξ (z) ≡ ∂ z and ξ (φ) ≡ ∂ φ , whose orbits generate translations and rotations with respect to the axis of symmetry, respectively.…”