NUT Solution Research Articles

The nut solution as a gravitational dyon

Linearized theory suggests that the NUT solution of Einstein's equations corresponds to a source with both mass and dual mass i.e. to a gravitational dyon. This is born out by the striking identity between the Killing operators of the NUT solution and the ‘total angular momentum’ operators of the monopole. On this basis, Misner's periodic time condition is shown to be the analogue of the Dirac quantization, and results from the requirement that the generators integrate to a global Lie group. It is also shown that there are no bound states for a Klein-Gordon field in NUT space provided the field vanishes in the conventional way at the horizon. For this purpose a generalized ‘tortoise coordinate’ is introduced.

Infilling for NUT Space

A method of generating interior NUT solutions from spherically symmetric ones is presented. It is similar to the well-known ``derivation'' of the corresponding vacuum metric from the Schwarzschild solution. These sources turn out to consist of material bridges, joining otherwise independent vacuum regions through a ``wormhole.'' It is shown that this matter cannot have an equation of state which is physically reasonable everywhere.

Interior Solution for a Finite Rotating Body of Perfect Fluid

An axially symmetric, stationary, type-$D$ solution of Einstein's field equations has been found which represents the superposition of a Kerr-NUT metric and a rigidly rotating perfect fluid in the same space-time region, analogous to the Newtonian superposition of the gravitational fields of a mass point, or ring, and a surrounding body of distributed matter. A fairly large family of old and new metrics are thus included as special cases: Schwarzschild, NUT, and Kerr exterior solutions, and new interior solutions for a stationary body of fluid, either spherical and nonrotating, or rigidly rotating with arbitrary angular velocity.