What is the ruling on a man suffering from baldness wearing a wig, and is it permissible to perform prayer and Umrah while wearing it?

It is forbidden for a bald man (أصلع) or a man with alopecia (أقرع) to wear a wig, because it falls under the ruling of hair extensions (al-wasl), for which the Prophet, peace and blessings be upon him, cursed the one who practices it. This is indicated by the hadith of Ibn Umar, may Allah be pleased with them both, that the Messenger of Allah, peace and blessings be upon him, "cursed the one who does hair extensions (al-wasilah) and the one for whom they are done (al-mustawsilah), and the one who tattoos (al-washimah) and the one for whom it is done (al-mustawshimah)." As for someone who performs Hajj or Umrah and has no hair, it is recommended, though not obligatory, for him to pass a razor over his head.