Vacuum solution
Encyclopedia
A vacuum solution is a solution of a field equation
in which the sources of the field are taken to be identically zero. That is, such field equations are written without matter
interaction (i.e.- set to zero).
Field equation
A field equation is an equation in a physical theory that describes how a fundamental force interacts with matter...
in which the sources of the field are taken to be identically zero. That is, such field equations are written without matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
interaction (i.e.- set to zero).
Examples
- In Maxwell's theory of electromagnetismElectromagnetismElectromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
, a vacuum solution would represent the electromagnetic field in a region of space where there are no electromagnetic sources (charges and electric currents), i.e. where the current 4-vector vanishes:
- Einstein's theory of general relativityGeneral relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
where a vacuum solutionVacuum solution (general relativity)In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress-energy tensor also vanishes identically, so that no matter or non-gravitational fields are present.More generally, a...
would represent the gravitational field in a region of spacetime where there are no gravitational sources (masses), i.e. where the energy-momentum tensor vanishes:
- Kaluza-Klein vacuum (static) field equations
- Kasner vacuum solution
See also
- Maxwell's equations#In vacuum
- Kerr vacuum
- Einstein field equationsEinstein field equationsThe Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...
- Ernst vacuum
- Kasner metricKasner metricThe Kasner metric is an exact solution to Einstein's theory of general relativity. It describes an anisotropic universe without matter...
- Vacuum solution (general relativity)Vacuum solution (general relativity)In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress-energy tensor also vanishes identically, so that no matter or non-gravitational fields are present.More generally, a...