I have a stabbing chest pain behind heart and numbness of left arm. what could be the cause of this?

Many causes: Chest pain of any type should never be ignored. While there are many benign, minor causes of chest pain , it is a symptom that can indicate an underlying serious potentially fatal problem of coronary artery disease which can lead to a heart attack. Chest pain should always be fully evaluated by competent and experienced medical personnel and never assumed to be insiginificant until checked out.

Aorta?: Could be your aorta ... Would recommend consulting with your doctor for heart exam as well as some evaluation of your aorta (echocardiogram or ct scan with contrast) ...

Chest pain to arm: If pain is not reproduced by pressure on breast-ribs then the pain is from inside chest = all organs inside can cause same symptoms. But must instantly rule out heart problems as sudden death can occur. The other vital organs need be urgently inspected to find the diagnosis. No sensory nerve inside the body resulting in pain of imprecise location. Intensive testings still do not reveal cause of pa.