The conformal potential of the stationary axisymmetric vacuum

✍ Scribed by Z. Perjés

• Book ID: 101701284
• Publisher: John Wiley and Sons
• Year: 1986
• Tongue: English
• Weight: 367 KB
• Volume: 307
• Category: Article
• ISSN: 0004-6337
• DOI: 10.1002/asna.2113070522

✦ Synopsis

The conformal potential of the stationary axisymmetric vacuum %. Pl?l<JI?S, Budapest, Hungary Central Hesearcli 1 nstitute for L'hysics 111 a stationary axisyniiiietric vacuuiii gravitational field, the confornial structure oi t h o 3-space is dctcriiiiiietl by tho symnietric, trace free and divergence-less tensor Yik. Using the Killing vector Ki of the axisynimetry, the conformal potential [I can be defined by LI, i = I &ijkKjYkYK,. Conversely, the tensor Yik 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,tp = o in terms of the conformal potential. Introducing the Ernst potential as a complex cuordinatc, the cylindrical radius can be eliniinatecl from the field equations.

Fuzzy Outlines of a Conformal Method

$1 ost if not ;ill of the proposed solution schemes for the stationary axisyiiiiiictric vacuum equations of general relativity include the static subclass as a smooth limiting case (see KKAMER et al. 1980). However, on purely phy-