I'm unsure as to whether this is a black rat or a native rat? The wildlife camera has caught the creature scurrying up and down this particular tree over a number of weeks.
I suggest its a black rat - the tail is long (longer than the head/body), the ears are large (the test is if folded forward they go past the middle of the eye - hard sometimes to determine from photos) and the head is pointed. Also black rats are very good climbers.