content_image/364177.jpg content_image/364178.jpg content_image/364179.jpg content_image/364181.jpg content_image/364180.jpg content_image/364182.jpg content_image/364183.jpg content_image/364184.jpg
## IV. THE BUBBLE SOLUTION 

We begin by considering the action 

<img src='content_image/364177.jpg'>

with metric 

<img src='content_image/364178.jpg'>

and scalar field 

<img src='content_image/364179.jpg'>

The O (3 , 1) × U (1) symmetry of the bubble of nothing is easily seen within this ansatz. We arrive at the equations 

and 

having denoted 

<img src='content_image/364181.jpg'>

<img src='content_image/364180.jpg'>

<img src='content_image/364182.jpg'>

The Einstein tensor then becomes 

<img src='content_image/364183.jpg'>

and the energy momentum tensor is given by 

<img src='content_image/364184.jpg'>

