Are non-synchronised static methods thread safe if they don't modify static class variables?
This method is 100% thread safe, it would be even if it wasn't static. The problem with thread-safety arises when you need to share data between threads - you must take care of atomicity, visibility, etc.
This method only operates on parameters, which reside on stack and references to immutable objects on heap. Stack is inherently local to the thread, so no sharing of data occurs, ever.
Immutable objects (String in this case) are also thread-safe because once created they can't be changed and all threads see the same value. On the other hand if the method was accepting (mutable) Date you could have had a problem. Two threads can simultaneously modify that same object instance, causing race conditions and visibility problems.
A method can only be thread-unsafe when it changes some shared state. Whether it's static or not is irrelevant.
The function is perfectly thread safe.
If you think about it... assume what would happen if this were different. Every usual function would have threading problems if not synchronized, so all API functions in the JDK would have to be synchronized, because they could potentially be called by multiple threads. And since most time the app is using some API, multithreaded apps would effectively be impossible.
This is too ridiculous to think about it, so just for you: Methods are not threadsafe if there is a clear reason why there could be problems. Try to always think about what if there were multiple threads in my function, and what if you had a step-debugger and would one step after another advance the first... then the second thread... maybe the second again... would there be problems? If you find one, its not thread safe.
Please be also aware, that most of the Java 1.5 Collection classes are not threadsafe, except those where stated, like ConcurrentHashMap.
And if you really want to dive into this, have a close look at the volatile keyword and ALL its side effects. Have a look at the Semaphore() and Lock() class, and their friends in java.util.Concurrent. Read all the API docs around the classes. It is worth to learn and satisfying, too.
Sorry for this overly elaborate answer.