Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the force between rotating co-axial black holes

Author: Gilbert Weinstein
Journal: Trans. Amer. Math. Soc. 343 (1994), 899-906
MSC: Primary 83C57
MathSciNet review: 1214787
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the force between rotating coaxial black holes, as it was defined in [9 and 10]. We show that under a certain limit, the force is attractive, and in fact tends to infinity. This lends support to the conjecture that the force is always positive.

References [Enhancements On Off] (What's this?)

  • [1] R. Bach and H. Weyl, Neue Lösungen der Einsteinschen Gravitationsgleichungen, Math. Z. 13 (1921), 132-145.
  • [2] B. Carter, Black hole equilibrium states, in Black Holes (C. DeWitt and B. S. DeWitt, eds.), Gordon and Breach, New York, 1973. MR 0465047 (57:4960)
  • [3] -, Bunting identity and Mazur identity for nonlinear systems including the black hole equilibrium system, Comm. Math. Phys. 99 (1985), 563-591. MR 796013 (87a:83049)
  • [4] S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge Univ. Press, Cambridge, 1973. MR 0424186 (54:12154)
  • [5] Y. Li and G. Tian, Regularity of harmonic maps with prescribed asymptotic behavior and applications, Comm. Math. Phys. 149 (1992), 1-30. MR 1182409 (94f:58036)
  • [6] -, Nonexistence of axially symmetric, stationary solution of Einstein vacuum equation with disconnected symmetric event horizon, Manuscripta Math. 73 (1991), 83-89. MR 1124312 (92m:83022)
  • [7] R. Penrose, Some unsolved problems in classical general relativity, in Seminar on Differential Geometry (S. T. Yau, ed.), Ann. of Math. Studies, no. 102, Princeton Univ. Press, Princeton, N.J., 1982. MR 645761 (83c:83001)
  • [8] D. C. Robinson, Uniqueness of the Kerr black hole, Phys. Rev. Lett. 34 (1975), 905-906.
  • [9] G. Weinstein, On rotating black holes in equilibrium in general relativity, Comm. Pure Appl. Math. 43 (1990), 903-948. MR 1072397 (91h:83063)
  • [10] -, The stationary axisymmetric two-body problem in general relativity, Comm. Pure Appl. Math. 45 (1992), 1183-1203. MR 1177481 (93k:83010)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 83C57

Retrieve articles in all journals with MSC: 83C57

Additional Information

Keywords: Black holes, Einstein's vacuum equations, stationary, rotation
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society