There is no definitive list of thread-safe classes in Java. The only people who could produce a definitive list would be Oracle1, and they haven't done so.
1 - Oracle is the custodian of both the reference Java class libraries (including javadocs), other "official" documentation and .. the official compliance test suite for Java. They are the people who would say whether a class (or subset of a class) that is thread-safe, is thread-safe by design, or whether it is merely a implementation artefact. Nobody else can make that calll with total certainty; i.e. whether a class that is thread-safe in the standard Oracle codebase should also be thread-safe in Harvest / Android codebase or the Classpath codebase, or ...