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In order for this geometry to represent an instability of the Kaluza – Klein vacuum, it must have the same asymptotics as the pure compactification, in particular the same (zero) value of Schwarzschild mass. This can be seen to be the case in a number of ways. The KK compactification possesses the eleven isometeries of Poincar´ e × U (1), which are broken down to the seven in O (3 , 1) × U (1) by the bubble of nothing (four translations are lost). This remaining symmetry is nevertheless larger than the five isometeries found in a generic Schwarzschild – Kaluza – Klein spacetime: O (3) × ❘ × U (1), and so the mass of the bubble must be zero. Hence, barring any symmetry in place to prevent bubble nucleation, the KK vacuum is unstable. 

## III. BUBBLE OF NOTHING IN A 5 d FLUX COMPACTIFICATION 

In this section we will discuss the construction of a bubble of nothing geometry similar to that presented above, but with one crucial difference: we will stabilize the Kaluza – Klein radion. This is accomplished by introducing an axionic flux winding around the extra dimension. The simplest example of this type of flux compactification was described in [12] using the action for a complex scalar field given by 

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