Progress in relativistic gravitational theory using the inverse scattering method

Abstract

The increasing interest in compact astrophysical objects (neutron stars, binaries, galactic black holes) has stimulated the search for rigorous methods, which allow a systematic general relativistic description of such objects. This paper is meant to demonstrate the use of the inverse scattering method, which allows, in particular cases, the treatment of rotating body problems. The idea is to replace the investigation of the matter region of a rotating body by the formulation of boundary values along the surface of the body. In this way we construct solutions describing rotating black holes and disks of dust ("galaxies"). Physical properties of the solutions and consequences of the approach are discussed. Among other things, the balance problem for two black holes can be tackled.

31 pages, 5 figures, to appear in J. Math. Phys

References in corpus (4)

• General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions
• Asymptotically flat solutions to the Ernst equation with reflection symmetry
• The Post-Newtonian Approximation of the Rigidly Rotating Disc of Dust to Arbitrary Order
• Black holes: A physical route to the Kerr metric

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