Static fluid cylinders and their fields: global solutions

Abstract

Abstract. The global properties of static perfect-fluid cylinders and their external Levi-Civita fields are studied both analytically and numerically. The existence and uniqueness of global solutions is demonstrated for a fairly general equation of state of the fluid. In the case of a fluid admitting a non-vanishing density for zero pressure, it is shown that the cylinder's radius has to be finite. For incompressible fluid, the field equations are solved analytically for nearly Newtonian cylinders and numerically in fully relativistic situations. Various physical quantities such as proper and circumferential radii, external conicity parameter and masses per unit proper/coordinate length are exhibited graphically.

Conformally flat sources for the Linet–Tian spacetime

“…Hence, it is possible to match a conformally flat static cylindrically symmetric interior spacetime (29) and (30), satisfying regularity conditions (12), to an exterior LT spacetime with Λ > 0, across a timelike cylindrical hypersurface S.…”

Brans-Dicke cylindrical wormholes

“…Thus Einstein's solution [24] corresponds to n ¼ 1 which gives a uniform scalar field ¼ 0 . For n ¼ 1 and c ¼ 0 the well-known Levi-Civita solution is obtained, which can be put in the form pointed out above by means of a suitable coordinate change [25]. When 2d À n þ 1 Þ 0, the metric is singular at r s ¼ c À2=ð2dÀnþ1Þ ; then this radius should be excluded as a possible throat radius.…”

Levi–civita Spacetimes in Multidimensional Theories

“…These spacetimes have been widely discussed in the literature from different standpoints, ranging from quantum singularities [2] to wormholes [3]. Although there has been some controversy regarding the physical interpretation and range of m and C, the Levi-Civita solution (1) is usually interpreted as the spacetime generated by infinite line masses and idealized cosmic strings [1], [4]- [8].…”

“…First, we obtain the most general static cylindrically symmetric vacuum solutions of the Einstein field equations in (4 + N ) dimensions. Second, under the assumption of separation of variables, we construct a time-dependent family of vacuum solutions in (4 + N ) that generalize (1). Third, we discuss the question of how these multidimensional solutions reduce to 4D.…”

“…When all the coefficients w (i) (s (i) ) are zero it reduces to the Levi-Civita solution (1) with N flat, and therefore innocuous, extra dimensions. Thus, (11) generalizes Levi-Civita's spacetimes to (4 + N ) dimensions.…”