JKR Contact Mechanics Theory (contd...)

How does the pressure distribution then alter from that in the Hertzian contact between surfaces without any interaction. The pressure distribution in that case was found to be

which resulted in total displacement at the interface of the form

It was observed that pressure distribution could have a component of the form  which could have resulted in a constant displacement.

But it was discarded! Because, if were positive, it would result in interference of surfaces outside the contact area.
On the other hand, if it were negative, infinite tension could not be sustained outside the contact area.