# Vacuum solution

The jargon word vacuum solution applies in physics to a solution of a field equation in the event that the source generating the field is identically zero everywhere, except at a single point. One speaks of a point charge . Mathematically, such fields can be modeled analytically with the Dirac delta distribution .

## Electromagnetism

In the case of Maxwell's equations of electromagnetism , a vacuum solution represents the electromagnetic field in a region of space in which there are no electrical charges ( ) and no currents ( ) or in covariant form :${\ displaystyle \ phi = 0}$${\ displaystyle {\ vec {j}} = 0}$${\ displaystyle j ^ {\ mu} = 0.}$

## theory of relativity

Another example is Einstein's general theory of relativity . In this case, a vacuum solution represents the gravitational field in a region of space-time that has no mass (except for a single point) ; H. for the energy-momentum tensor applies everywhere (except for one point):

${\ displaystyle T ^ {\ mu \ nu} = 0.}$

The most important vacuum solutions of ART are the Schwarzschild metric and the Kerr metric .