Abstract
There has been no Kerr-like solution to Rosen's bimetric theory of gravity, in the sense that there is no stationary, axially symmetric solution with angular momentum term. Here such a solution is derived and investigated.
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References
Courant, R., and Hilbert, D. (1962).Methods of Mathematical Physics, Interscience, New York.
Dewitt, B. S. (1967). Quantum theory of gravity, I, The canonical theory,Physical Review,160, 1113–1148.
Eells, J., and Lemaire, L. (1978). A report on harmonic maps,Bulletin of the London Mathematical Society,10, 1–68.
Eells, J., and Lemaire, L. (1980).Selected Topics in Harmonic Maps, Tulane, CBMS Regional Conference Series #50.
Eells, J., and Sampson, J. H. (1964). Harmonic mappings of Riemannian manifolds,American Journal of Mathematics 86, 109–160.
Fuller, F. B. (1954). Harmonic mappings,Proceedings of the National Academy of Science of the USA,40, 987–991.
Knill, R., Kalka, M, and Sealey, H. (1982).Proceedings of the Tulane Harmonic Maps Conference, Springer-Verlag Lecture Notes in Mathematics #949, New York.
Kobayaski, S., and Nomizu, K. (1963).Foundations of Differential Geometry, Wiley, New York.
Matzner, R. A., and Misner, C. W. (1967). Gravitational field equations for sources with axial symmetry and angular momentum,Physical Review,154, 1229–1232.
Misner, C. W. (1978). Harmonic maps as models for physical theories,Physical Review D,18, 4510–4523.
Rosen, N. (1973). A Bi-metric theory of gravitation,General Relativity and Gravitation 4, 435–447.
Rosen, N. (1974). A theory of gravitation,Annals of Physics,84, 455–473.
Rosen, N. (1975). A Bi-metric theory of gravitation, II,General Relativity and Gravitation,6, 259–268.
Rosen, N. (1980). General Relativity with a background metric,Foundations of Physics,10, 673–704.
Sampson, J. H. (1978). Some properties and applications of harmonic mappings,Annales Scientifiques de l'Ecole Normale Supérieure,11, 211–228.
Stoeger, W. R. (1983). Rosen's bi-metric theory of gravity as a harmonic map, inProceedings of the third Marcel Grossmann Meeting on Recent Developments in General Relativity, Hu Ning, ed. Part B, pp. 921–925, North-Holland, Amsterdam.
Stoeger, W. R. (1978). Orbital topography and other astrophysical consequences of Rosen's bi-metric theory of gravity,General Relativity and Gravitation 9, 165–174.
Stoeger, W. R. (1979). Axisymmetric accretion flows very near black holes and Rosen-collapsed objects,General Relativity and Gravitation 10, 671–679.
Stoeger, W. R. (1980). Rapid variability, dying pulse train, and black holes,Monthy Notices of the Royal Astronomical Society 190, 715–772.
Whitman, A., Knill, R., and Stoeger, W. (1986). Some harmonic maps on pseudo-Riemannian manifolds,International Journal of Theoretical Physics,25, 1139–1153.
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Knill, R.J., Stoeger, W.R. & Whitman, A.P. Axially symmetric solution to Rosen's field equations with angular momentum. Int J Theor Phys 27, 283–288 (1988). https://doi.org/10.1007/BF00670755
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DOI: https://doi.org/10.1007/BF00670755