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:

A)    
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.

B)     
Farm A needs to be made aware of alternate access mappings defined in farm B.

How:
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. 

References:

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