A Charged Rotating Cylindrical Shell

Abstract

We give an example of a spacetime having an infinite thin rotating cylindrical shell constituted by a charged perfect fluid as a source. As the interior of the shell the Bonnor-Melvin universe is considered, while its exterior is represented by Datta-Raychaudhuri spacetime. We discuss the energy conditions and we show that our spacetime contains closed timelike curves. Trajectories of charged test particles both inside and outside the cylinder are also examined. Expression for the angular velocity of a circular motion inside the cylinder is given.

Gravitational Collapse of a Rotating Cylindrical Null Shell in the Cosmic String Spacetime

“…A number of papers have been concerned with stationary and non-stationary rotating cylindrical shells in general relativity (see Refs. [1,2] and references therein). In particular, by considering the collapse of a cylindrical shell made of pressure-free counter-rotating particles in vacuum, the authors showed that even a small amount of rotation can halt the collapse at some minimal non-zero radius.…”

Electrovacuum cylindrical stationary solutions in general relativity

“…This solution corresponds to the Datta-Raychaudhuri solution [9]. With the help of coordinate transformation we can write β 2 = 0.…”

“…where k 1 , k 2 are constants of integration. This solution is equivalent to the Datta and Raychaudhuri solution [9], where k 1 = 0 and 2αC 2 2 = 4. A special case of αC 2 = 0, k 2 = 0 gives the solution mentioned in section 5.3.…”

Estudo gravimétrico do Município de Fortaleza e do Campus do Pici – Universidade Federal do Ceará, Fortaleza, CE, Brasil

“…Furthermore, a solution or model of particular relevance in GR is the so-called Bonnor-Melvin spacetime (or Bonnor-Melvin universe), which is an exact solution of Einstein-Maxwell equations that describes a static and cylindrically symmetric (electro)magnetic field immersed in its own gravitational field (where the magnetic field is aligned with the symmetry axis) [63][64][65][66][67][68]. That is, the Bonnor-Melvin spacetime (can also be called Bonnor-Melvin magnetic spacetime) describes the gravitational field generated by an axial magnetic field permeating the whole spacetime due to the azimuthal current on the surface of a coaxial cylinder enveloping part of the spacetime [69].…”