Static Axially Symmetric Einstein-Yang-Mills-Dilaton Solutions: I.Regular Solutions

Details Static Axially Symmetric Einstein-Yang-Mills-Dilaton Solutions: I.Regular Solutions Static Axially Symmetric Einstein-Yang-Mills-Dilaton Solutions: I.Regular Solutions

1997-07-19

arxiv.org/abs/gr-qc/9707045v1

Phys.Rev. D57 (1998) 834-856

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

76 pages, including 51 postscript figures, RevTex format

Scientific paper

10.1103/PhysRevD.57.834

We discuss the static axially symmetric regular solutions, obtained recently in Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theory [1]. These asymptotically flat solutions are characterized by the winding number $n>1$ and the node number $k$ of the purely magnetic gauge field. The well-known spherically symmetric solutions have winding number $n=1$. The axially symmetric solutions satisfy the same relations between the metric and the dilaton field as their spherically symmetric counterparts. Exhibiting a strong peak along the $\rho$-axis, the energy density of the matter fields of the axially symmetric solutions has a torus-like shape. For fixed winding number $n$ with increasing node number $k$ the solutions form sequences. The sequences of magnetically neutral non-abelian axially symmetric regular solutions with winding number $n$ tend to magnetically charged abelian spherically symmetric limiting solutions, corresponding to ``extremal'' Einstein-Maxwell-dilaton solutions for finite values of $\gamma$ and to extremal Reissner-Nordstr\o m solutions for $\gamma=0$, with $n$ units of magnetic charge.

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