# 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

- ↑ Guillermo A González and Antonio C. Gutiérrez-Piñeres. (2012). "Stationary axially symmetric relativistic thin discs with nonzero radial pressure".
*Classical and Quantum Gravity*.**29**(13): 13500. Bibcode:2012CQGra..29m5001G. doi:10.1088/0264-9381/29/13/135001. - ↑ Antonio C. Gutiérrez-Piñeres, Guillermo A González and Hernando Quevedo . (2013). "Conformastatic disk-haloes in Einstein-Maxwell gravity".
*Phys. Rev. D*.**87**(4): 044010. arXiv:1208.0010. Bibcode:2013PhRvD..87a4010C. doi:10.1103/PhysRevD.87.014010.