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 … Show more
“…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.…”
Section: Casementioning
confidence: 97%
“…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).…”
Section: Circular Geodesics In the Weyl Classmentioning
confidence: 99%
“…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].…”
Section: Geodesics In the Weyl Classmentioning
confidence: 99%
“…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.…”
The geodesic equations are integrated for the Lewis metric and the effects of the different parameters appearing in the Weyl class on the motion of test particles are brought out. Particular attention deserves the appearance of a force parallel to the axial axis and without Newtonian analogue.
“…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.…”
Section: Casementioning
confidence: 97%
“…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).…”
Section: Circular Geodesics In the Weyl Classmentioning
confidence: 99%
“…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].…”
Section: Geodesics In the Weyl Classmentioning
confidence: 99%
“…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.…”
The geodesic equations are integrated for the Lewis metric and the effects of the different parameters appearing in the Weyl class on the motion of test particles are brought out. Particular attention deserves the appearance of a force parallel to the axial axis and without Newtonian analogue.
“…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].…”
Abstract. Dirac's constraint analysis and the symplectic structure of geodesic equations are obtained for the general cylindrically symmetric stationary spacetime. For this metric, using the obtained first order Lagrangian, the geodesic equations of motion are integrated, and found some solutions for Lewis, Levi-Civita, and Van Stockum spacetimes.
We discuss gravitomagnetism in connection with rotating cylindrical systems. In particular, the gravitomagnetic clock effect is investigated for the exterior vacuum field of an infinite rotating cylinder. The dependence of the clock effect on the Weyl parameters of the stationary Lewis metric is determined. We illustrate our results by means of the van Stockum spacetime.
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