The Einsteinian gravitational field of the rigidly rotating disk of dust

Journal of Mathematical Physics

Meinel

2003

Self Cite

105

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.

Section: Solution Of the Direct Problem A Axis And Infinitymentioning

confidence: 88%

“…This relation interlinks F (K) and G(K) and, because of (34),(35) real and imaginary part of the axis values f (ζ) of the Ernst potential 16,17 .…”

Section: Cf (31)mentioning

confidence: 92%

Progress in relativistic gravitational theory using the inverse scattering method

Journal of Mathematical Physics

Meinel

2003

Self Cite

105

“…The free boundary value problem for the relativistic rigidly rotating disk of dust was approximately discussed by Bardeen and Wagoner [4,5] and analytically solved in terms of ultraelliptic theta functions by Neugebauer and Meinel [1,2,3] using the Inverse Scattering…”

Section: Rigidly Rotating Disks Of Dustmentioning

confidence: 99%

“…To get explicit expressions for these "equations of state" we make use of the disk of dust solution [1,2,3] to obtain…”

Section: Rigidly Rotating Disks Of Dustmentioning

confidence: 99%

“…From a mathematical point of view they are solutions to boundary value problems of the Einstein equations. Explicit solutions in terms of standard functions or integrals are known for rigidly rotating disks of dust [1,2,3,4,5] (the only known solutions for isolated rigidly rotating bodies) and counter-rotating disks of dust, consisting of clockwise and counter-clockwise rotating dust particles (see e.g. [6], [7] or [8]).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Collisions of rigidly rotating disks of dust in general relativity

Hennig

2006

Phys. Rev. D

Rotating bodies as boundary value problems

2000

Ann. Phys.

Self Cite

There are physically interesting particular cases in which the treatment of the matter region of rotating bodies may be replaced by the formulation of boundary values along the surface of the body. In this way, rotating black holes and rotating disks of dust ("galaxies") are described by boundary value problems which can be solved by means of the so-called Inverse Scattering Method. 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.