To be precise, garbage collectors are a problem for real-time systems. To be even more precise, it is possible to write real-time software in languages that have automatic memory management.
More details can be found in the Real Time Specification for Java on one of the approaches for achieving real-time behavior using Java. The idea behind RTSJ is very simple – do not use a heap. RTSJ provides for new varieties of Runnable objects that ensure threads do not access heap memory of any kind. Threads can either access scoped memory (nothing unusual here; values are destroyed when the scope is closed) or immortal memory (that exists throughout the application lifetime). Variables in the immortal memory are written over, time and again with new values.
Through the use of immortal memory, RTSJ ensures that threads do not access the heap, and more importantly, the system does not have a garbage collector that preempts execution of the program by the threads.
More details are available in the paper “Project Golden Gate: Towards Real-Time Java in Space Missions” published by JPL and Sun.