Is it permissible for a man to learn Torah without a Kippah?
Let's say that he can't wear a Kippah at work, or he lives someplace where it is dangerous to outwardly display signs of being Jewish, yet, for whatever reason, picking up a Sefer, or logging on to Mi Yodeya, would go unnoticed. Would this be ok to do?
אף-על-פי שבודאי שאין ללמוד תורה בגילוי ראש, מכל מקום אין זה מעיקר הדין, אך יש להזהר בזה מאד, ואפי' כשלומד לבד בחדרו. [שו''ת יביע אומר ח''ו חאו''ח סי' טו סק''ז]
Meikar Hadin (according to the letter of the law) one isn't obligated to learn with a head covering: nevertheless, one should certainly wear a head covering while learning (even alone in his room).
"Even though one should certainly not learn Torah without a head covering, nevertheless this isn't from the letter of the law. However, one should be very meticulous with this even in his own room."
