Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

REFERENCES 75
5. DISCUSSION
The analytical solution for the rigidly rotating disk of dust in general
relativity described above has been found by applying soliton–theoretical
solution techniques to the Ernst equation. These methods only work for
the vacuum equations however. Therefore, genuine perfect fluid configurations,
e.g. models of rotating neutron stars, can only be treated
numerically so far. However, there are some possible analytical generalizations
of the disk solution considered that might be interesting:
(i) Differentially rotating disks of dust and (ii) black holes surrounded
by dust rings. The first item has already been handled succesfully by a
mixture of analytical and numerical methods [16, 17].
Acknowledgments
The support from the DFG is gratefully acknowledged.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
G. Neugebauer and R. Meinel, Astrophys. J. 414 (1993) L97.
G. Neugebauer and R. Meinel, Phys. Rev. Lett. 73 (1994) 2166.
G. Neugebauer and R. Meinel, Phys. Rev. Lett. 75 (1995) 3046.
L. Lichtenstein, “Gleichgewichtsfiguren rotierender Flüssigkeiten”, (Springer,
Berlin, 1933).
S. Chandrasekhar, “Ellipsoidal figures of equilibrium”, (Dover, New York 1969).
I. Newton, “Philosophiae naturalis principle”, Book III, Propositions XVIII–XX.
(1686).
I. Kant, “Allgemeine Naturgeschichte und Theorie des Himmels” (1755).
C. Maclaurin, “A Treatise on Fluxions”, (1742).
G. Neugebauer, A. Kleinwächter and R. Meinel, Helv. Phys. Acta 69 (1996) 472.
A. Kleinwächter (2001), this volume.
J.M. Bardeen and R.V. Wagoner, Astrophys. J. 158 (1969) L65.
J.M. Bardeen and R.V. Wagoner, Astrophys. J. 167 (1971) 359.
D. Petroff and R. Meinel Phys. Rev. D. (2000), submitted.
R. Meinel, in: Recent Development in Gravitation and Mathematical Physics,
Eds. A. Garcia et al., (Science Network Publishing Konstanz, 1998). [grqc/9703077].
[15] R. Meinel, Ann. Phys. (Leipzig) 9 (2000) 335.
[16] M. Ansorg and R. Meinel, Gen. Rel. Grav. 32 (2000) 1365.
[17] M. Ansorg, Gen. Rel. Grav. (2001) in the press [gr-qc/0006045].