are there fake celebrity email addresses with someone impersonating the celebrity?

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Are there fake celebrity email addresses posted on the internet with someone impersonating the celebrity? A real celebrity would never make their email address available to the public would they? It is impossible to get a celebrity's email address isn't it? Don't they keep that private? If you do see a celebrity's email address on the internet it's not really the celebrity right? If there are fake celebrity email addresses on the internet and someone is impersonating the celebrity is that illegal? Has anyone heard of someone emailing someone they thought was a celebrity and got emails back and they found out it wasn't really the celebrity?