arXiv subjects

A. Z. Wang

Publications and source records attributed to A. Z. Wang.

6 recordsLinked to original sources

arXiv2002

Collapsing and Expanding Cylindrically Symmetric Fields with Ligh-tlike Wave-Fronts in General Relativity

The dynamics of collapsing and expanding cylindrically symmetric gravitational and matter fields with lightlike wave-fronts is studied in General Relativity, using the Barrabes-Israel method. As an application of the general formulae developed, the collapse of a matter field that satisfies the condition R_{AB}g^{AB} = 0, (A, B = z, phi), in an otherwise flat spacetime background is studied. In particular, it is found that the gravitational collapse of a purely gravitational wave or a null dust fluid cannot be realized in a flat spacetime background. The studies are further specified to the collapse of purely gravitational waves and the general conditions for such collapse are found. It is shown that after the waves arrive at the axis, in general, part of them is reflected to spacelike infinity along the future light cone, and part of it is focused to form spacetime singularities on the symmetry axis. The cases where the collapse does not result in the formation of spacetime singularities are also identified.

gr-qc↗

arXiv2002

Rotating cylindrical shell source for Lewis spacetime

Rotating thin-shell-like sources for the stationary cylindrically symmetric vacuum solutions (Lewis) are constructed and studied. It is found, by imposing the non existence of timelike curves in the exterior of the shell, and that the source satisfies the weak, dominant and strong energy conditions that the parameters, commonly denoted by $a$ and $σ$, are restricted to $0 \le σ\le 1/4$ when $a > 0$, or $1/4 \le σ\le 1/2$ when $a < 0$.

gr-qc↗

arXiv2001

On the interpretation of cylindrically symmetric Levi-Civita spacetime for 0<sigma<infinity

We study Levi-Civita metric for values of its sigma parameter in the range 0< sigma<infinity. We show that the value sigma=1/2 makes the axial and angular coordinates switch meaning. We present its geodesics and a physical source satisfying the energy conditions for all the range of sigma. This source allows us to obtain an energy per unit length which agrees with the behaviour of the geodesics and the fact that the solution has no event horizon.

gr-qc↗

arXiv2001

Gravitational collapse of spherically symmetric perfect fluid with kinematic self-similarity

Analytic spherically symmetric solutions of the Einstein field equations coupled with a perfect fluid and with self-similarities of the zeroth, first and second kinds, found recently by Benoit and Coley [Class. Quantum Grav. {\bf 15}, 2397 (1998)], are studied, and found that some of them represent gravitational collapse. When the solutions have self-similarity of the first (homothetic) kind, some of the solutions may represent critical collapse but in the sense that now the "critical" solution separates the collapse that forms black holes from the collapse that forms naked singularities. The formation of such black holes always starts with a mass gap, although the "critical" solution has homothetic self-similarity. The solutions with self-similarity of the zeroth and second kinds seem irrelevant to critical collapse. Yet, it is also found that the de Sitter solution is a particular case of the solutions with self-similarity of the zeroth kind, and that the Schwarzschild solution is a particular case of the solutions with self-similarity of the second kind with the index $α= 3/2$.

gr-qc↗

arXiv2001

Levi-Civita Solutions Coupled with Electromagnetic Fields

The local and global properties of the Levi-Civita (LC) solutions coupled with an electromagnetic field are studied and some limits to the vacuum LC solutions are given. By doing such limits, the physical and geometrical interpretations of the free parameters involved in the solutions are made clear. Sources for both the LC vacuum solutions and the LC solutions coupled with an electromagnetic field are studied, and in particular it is found that all the LC vacuum solutions with $σ\ge 0$ can be produced by cylindrically symmetric thin shells that satisfy all the energy conditions, weak, dominant, and strong. When the electromagnetic field is present, the situation changes dramatically. In the case of a purely magnetic field, all the solutions with $σ\ge 1/\sqrt{8}$ or $σ\le - 1/\sqrt{8}$ can be produced by physically acceptable cylindrical thin shells, while in the case of a purely electric field, no such shells are found for any value of $σ$.

gr-qc↗

arXiv1996

On parameters of the Levi-Civita solution

The Levi-Civita (LC) solution is matched to a cylindrical shell of an anisotropic fluid. The fluid satisfies the energy conditions when the mass parameter $σ$ is in the range $0 \le σ\le 1$. The mass per unit length of the shell is given explicitly in terms of $σ$, which has a finite maximum. The relevance of the results to the non-existence of horizons in the LC solution and to gauge cosmic strings is pointed out.

gr-qc↗