N-black hole stationary and axially symmetric solutions of the Einstein/Maxwell equations

Communications in Partial Differential Equations

Volumn 21, Issue 9-10, 1996, Pages 1389-1430

  Weinstein, Gilbert ^a  

^a UNIVERSITY OF ALABAMA AT BIRMINGHAM   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000841230     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309608821232     Document Type: Article

References (23)

1. R. BACH AND H. WEYL, Neue Lösungen der Einsteinschen Gravitationsgleichungen, Mathematische Zeitschrift 13 (1921), 132-145.
2. B. CARTER, Black Hole Equilibrium States, in Black Holes, edited by C. DeWitt and B. S. DeWitt, Gordon and Breach Science Publishers, New York, 1973.
3. B. CARTER, Bunting Identity and Mazur Identity for Nonlinear Systems Including the Black Hole Equilibrium System, Comm. Math. Phys. 99 (1985), 563-591.
4. P. T CHRUŚCIEL, "No Hair" Theorems - Folklore, Conjectures, Results, to appear in Proc. of AMS/CMS Conf on Diff. Geom. and Math. Phys., Vancouver, August 1993, Eds. J. Beem and K. Duggal, Contemporary Mathematics, AMS, 1994.
5. P. T. CHRUŚCIEL AND R. M. WALD, On the Topology of Black Holes, ESI preprint. Vienna, October 1994.
6. P. EBERLEIN AND B. O'NEILL, Visibility Manifolds, Pacific J. Math. 46 (1973), No. 1, 45-109.
7. F. J. ERNST, New Formulation of the Gravitational Field Problem, Phys. Rev. Letters 167 (1968), 1175-1178.
8. E. HEINTZE AND H. C. IM HOF, Geometry of Horospheres, J. Diff. Geom. 12 (1977), 481-491.
9. Y. LI AND G. TIAN, Nonexistence of Axially Symmetric. Stationary Solution of Einstein Vacuum Equation with Disconnected Symmetric Event Horizon, Manuscripts Math. 73 (1991), 83-89.
10. _, Regularity of Harmonic Maps with Prescribed Asymptotic Behavior and Applications, Comm. Math. Phys. 149 (1992), No. 1, 1-30.
11. S. D. MAJUMDAR, A Class of Exact Solutions of Einstein's Field Equations, Phy. Rev. 72 (1947), 390-398.
12. P. O. MAZUR, Proof of Uniqueness of the Kerr-Newman Black Holes, J. Phys. A 15 (1982), 3173-3180.
13. G. D. MOSTOW, Strong Rigidity of Locally Symmetric Spaces, Annals of Mathematics Studies, No. 78, Princeton University Press, Princeton, 1973.
14. A. PAPAPETROU, A Static Solution of the Equations of the Gravitational Field for an Arbitrary Charge-Distribution, Proc. Roy. Irish Acad. A51 (1947), 191-204.
15. R. PENROSE, Some Unsolved Problems in Classical General Relativity, in Seminar on Differential Geometry, edited by S. T. Yau, Annals of Mathematics Studies no. 102, Princeton University Press, Princeton 1982.
16. D. C. ROBINSON, Uniqueness of the Kerr Black Hole, Phys. Rev. Letters 34 (1975), 905-906.
17. R. SCHOEN AND K. UHLENBECK, A Regularity Theory for Harmonic Maps, J. Diff. Geom. 17 (1982), 307-335.
18. _, Boundary Regularity and the Dirichlet Problem for Harmonic Maps, J. Diff. Geom. 18 (1983), 253-268.
19. R. SCHOEN AND S. T. YAU, Compact Group Actions and the Topology of Manifolds with Non-Positive Curvature, Top. 18 (1979), 361-380.
20. G. WEINSTEIN, On Rotating Black Holes in Equilibrium in General Relativity, Comm. Pure Appl. Math. 43 (1990), 903-948.
21. _, The Stationary Axisymmetric Two-Body Problem in General Relativity, Comin. Pure Appl. Math. 45 (1992), 1183-1203.
22. _, On the Force between Rotating Co-Axial Black Holes, Trans. Amer. Math. Soc. 343 (1994), No. 2, 899-906.
23. _, On the Dirichlet Problem for Harmonic Maps with Prescribed Singularities, Duke Math. J. 77 (1995), No. 1, 135-165.