general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...

, the relativistic disk expression refers to a class of ''

axi-symmetric In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself. Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the ...

'' self-consistent solutions to

Einstein's field equations In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form ...

corresponding to the gravitational field generated by

isolated sources. To find such solutions, one has to pose correctly and solve together the ‘outer’ problem, a boundary value problem for vacuum

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. 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

General relativity Exact solutions in general relativity {{relativity-stub