Is it possible to have an org.apache.log4j.Logger field in a singleton class? Are there any concurrency issues due to sharing it between multiple threads?
No, there will be no problems, since it is thread safe (that is, it will not break if multiple threads access it at the same time).
See http://logging.apache.org/log4j/1.2/faq.html#a1.7
No, the Logger object can be used by multiple threads, have you had any problems?