Consider the following: You have 2 SharePoint 2010 farms, farm A and farm B. Farm A is hosting the search service application. Farm B is consuming the search service application from farm A. In farm B you have a web application that is extended on multiple zones. You want to index as few as possible URLs in order to have a small index and also reduce network load.
In order to achieve the above the following needs to be configured:
Using central administration of farm A in the SharePoint sites content source the public url of a zone.
Recommendation is to use a public url associated with a zone that uses windows integrated authentication and to use the public url of the default zone.
Farm A needs to be made aware of alternate access mappings defined in farm B.
Use the “Map to External Resource” option to create the same alternate access mappings as defined for the web application in farm B.
This configuration will allow you to index a single URL. The option Map to External Resource just creates alternate access mappings entries in the configuration database of farm A.
Map to External Resource http://technet.microsoft.com/en-us/library/cc263208(office.12).aspx
Plan for authentication http://technet.microsoft.com/en-us/library/cc262926.aspx#section3