Relativistic disk

In general relativity, the relativistic disk refer 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.

References

v t e Relativity Special relativity Background Principle of relativity Introduction to special relativity Special relativity Foundations Relative motion Frame of reference Speed of light 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 Minkowski spacetime World line Spacetime diagrams Light cone General relativity Background Introduction Mathematical formulation Resources Fundamental concepts Special relativity Equivalence principle World line Riemannian geometry Spacetime diagrams Spacetime in General relativity Phenomena Kepler problem Lenses Waves Frame-dragging Geodetic effect Event horizon Singularity Black hole Equations Linearized gravity Post-Newtonian formalism Einstein field equations Geodesic equation Friedmann equations ADM formalism BSSN formalism Hamilton–Jacobi–Einstein equation Advanced theories Kaluza–Klein Quantum gravity Solutions Schwarzschild Reissner–Nordström Gödel Kerr Kerr–Newman Kasner Taub-NUT Milne Robertson–Walker pp-wave van Stockum dust Scientists Einstein Lorentz Hilbert Poincaré Schwarzschild de Sitter Reissner Nordström Weyl Eddington Friedman Milne Zwicky Lemaître Gödel Wheeler Robertson Bardeen Walker Kerr Chandrasekhar Ehlers Penrose Hawking Taylor Hulse Stockum Taub Newman Yau Thorne others