Premium
The conformal potential of the stationary axisymmetric vacuum
Author(s) -
Perjés Z.
Publication year - 1986
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.2113070522
Subject(s) - conformal map , physics , conformal gravity , killing vector field , gravitational potential , conformal symmetry , vector potential , conformal geometry , rotational symmetry , mathematical physics , tensor (intrinsic definition) , gravitational field , vector field , gravitation , field (mathematics) , classical mechanics , mathematical analysis , geometry , quantum mechanics , mathematics , mechanics , pure mathematics , magnetic field
Abstract In a stationary axisymmetric vacuum gravitational field, the conformal structure of the 3‐space is determined by the symmetric, trace free and divergence‐less tensor Y ir . Using the Killing vector K i of the axisymmetry, the conformal potential U can be defined by U, i = εijk KjY kr K r . Conversely, the tensor Y ik is given algebraically in terms of the gradient U, i of the conformal potential. An attempt is made here to re‐formulate the field equations R λμ = 0 in terms of the conformal potential. Introducing the Ernst potential as a complex coordinate, the cylindrical radius can be eliminated from the field equations.