Relativistic disk

In general relativity, the relativistic disk expression refers to a class of axi-symmetric self-consistent solutions to Einstein's field equations corresponding to the gravitational field generated by axi-symmetric isolated sources. To find such solutions, one has to pose correctly and solve together the ‘outer’ problem, a boundary value problem for vacuum Einstein's field equations whose solution determines the external field, and the ‘inner’ problem, whose solution determines the structure and the dynamics of the matter source in its own gravitational field. Physically reasonable solutions must satisfy some additional conditions such as finiteness and positiveness of mass, physically reasonable kind of matter and finite geometrical size.^[1][2] Exact solutions describing relativistic static thin disks as their sources were first studied by Bonnor and Sackfield and Morgan and Morgan. Subsequently, several classes of exact solutions corresponding to static and stationary thin disks have been obtained by different authors. The thermodynamics of a thin disk surrounded by a halo in presence of an electromagnetic field is presented in http://arxiv.org/abs/1306.6591v2.

References

Relativity
Special relativity	Background Principle of relativity Special relativity Foundations Frame of reference Speed of light Hyperbolic orthogonality Rapidity Maxwell's equations Formulation Galilean relativity Galilean transformation Lorentz transformation Consequences Time dilation Relativistic mass Mass–energy equivalence Length contraction Relativity of simultaneity Relativistic Doppler effect Thomas precession Relativistic disks Spacetime Light cone World line Spacetime diagram Biquaternions Minkowski space
General relativity	Background Introduction Mathematical formulation Fundamental concepts Special relativity Equivalence principle World line Riemannian geometry Minkowski diagram Phenomena Black hole Event horizon Frame-dragging Geodetic effect Lenses Singularity Waves Ladder paradox Twin paradox Two-body problem Equations ADM formalism BSSN formalism Einstein field equations Geodesic equation Friedmann equations Linearized gravity Post-Newtonian formalism Hamilton–Jacobi–Einstein equation Advanced theories Brans–Dicke theory Kaluza–Klein Mach's principle Quantum gravity Solutions Schwarzschild (interior) Reissner–Nordström Gödel Kerr Kerr–Newman Kasner Taub–NUT Milne Robertson–Walker pp-wave van Stockum dust Weyl−Lewis−Papapetrou
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