Certificate revocation When someone claims that the private key corresponding to the public key  has been stolen, and sends to the CA a statement of this fact signed with respect to public key pk.

Why doesn't the CA need to check his identity in this case, and why is there no concern

that the person who has stolen his key can forge signatures with respect to pk?
There are two cases to distinguish: The attacker issues the revokation or the owner issues the revokation.


Attacker revoking the cert. In this case the attacker has the private key and uses this to issue a revokation. He thus effectively takes any use out he could get out of theh certificate and the certificate is revoked as it should be in such a situation."Thank you attacker, you just did my job  without me having noticed the breach!"
Owner revoking the cert. The owner wants to prevent missuse of the cert and thus revokes it. This stops the attacker. Everything as it's supposed to be.