If you have you Sharepoint 2010 Farm setup in one domain & your users are in a seperate domain using a one way trust, when they perform a search they will not return any search results. This is because the account running the app pool for the search query service is running using a domain account on the trusting domain.
This account has no rights on the domain where the users sit to determine how the search results should be security trimmed etc. My initital thought was we need to run the search query app pool account using an account on the same domain as the users which does / will work.
However a better way is to run the following powershell command:
now run a ‘Full Crawl’ and you users should now return search results as expected over the one way trust.
You can display you Search App details with the following command:
Note: After performing the above search alerts will be broken. If you do need search alerts you can try running your search app pool with an account from the user domain.