The parameters of the Lewis metric for the Weyl class

Abstract

Author's internet addresses respectively: mfas@on.br, lherrera@conicit.ve, fmpaiva@on.br and nos@on.br. AbstractWe provide physical interpretation for the four parameters of the stationary Lewis metric restricted to the Weyl class. Matching this spacetime to a completely anisotropic, rigidly rotating, fluid cilinder, we obtain from the junction conditions that one of these parameters is proportional to the vorticity of the source. From the Newtonian approximation a second parameter is found to be proportional to the energy per unit of length. The remaining two parameters may be associated to a gravitational analog of the Aharanov-Bohm effect.We prove, using the Cartan scalars, that the Weyl class metric and static Levi-Civita metric are locally equivalent, i.e., indistinguishable in terms of its curvature.

Geodesics in Lewis space–time

“…The term c/(1 − 4σ) represents an inertial frame dragging correction to the static case, similar to the one appearing in the case of the Kerr metric [7] or in the field of a massive charged magnetic dipole [8]. The presence of c in that term, becomes intelligible when we recall that this parameter measures the vorticity of the source when described by a rigidly rotating anisotropic cylinder [3]. It increases or diminishes the modulus of ω if the vorticity is in the same or oposite direction, respectively, of the rotation of the test particle.…”

“…All these interpretations are restricted to the Weyl class only. For further details see reference [3]. We shall now discuss the expression for the angular velocity (49) and the tangential velocity (53).…”

“…We restrict the study of geodesics to 0 < n < 1, which is the condition for circular timelike geodesics as expected in the Newtonian analog [3].…”

“…Usually this metric is presented with four parameters [2] which may be real (Weyl class) or complex (Lewis class). In recent papers [3,4], the physical meaning of these parameters have been discussed for both classes. Thus for the Weyl class, it appears that one of the parameters is proportional to the energy per unit length (at least in the Newtonian limit), a second parameter is the arbitrary constant potential which is always present in the Newtonian solution, and the remaining two parameters are responsible for the non staticity of the metric, although affecting staticity in different ways.…”

Dirac Analysis and Integrability of Geodesic Equations for Cylindrically Symmetric Spacetimes

“…Lewis stationary vacuum metric is usually presented with four parameters [14] which admits a specific physical interpretation when matched to a particular source. These four parameters which are related to topological defects [9,15] not entering into the expression of the physical components of curvature tensor may be real (Weyl class) or complex (Lewis class). In recent years, the physical meaning of these parameters have been discussed for both classes [9,10].…”