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To have the repository content consistent with the search index and value storate, the repository should be suspened. It means all working threads are suspended until resume operation performed. Index will be flushed.
JCR provides ability to suspend repository via JMX.
To suspend repository just need to invoke suspend() operation. The returned result will be "suspended" if everything passed successfully.
The result "undefined" means not all components successfully suspended, check console to see stacktraces.
Now we can backup content manually or using third part software. We need to backup:
Database
Lucene index
Value storage (if configured)