It’s your viva day. There’s you, your internal examiner, your external examiner. At some institutions there’s an independent chair too, someone making sure that the viva is fair. Many universities also allow a candidate’s supervisor to be present.
Did you hear that?! That was the sharp intake of breath of a thousand PhDs around the land.
My supervisor could be at my viva?! Noooooooo!!!
If your supervisor came to your viva they would be there only as an observer. If they came to your viva they couldn’t ask any questions or comment on your responses. If they came it would only be because you allowed it.
But if they came they would be able to make notes on your behalf. You’re free to make any notes you like, but that could be tricky. Your supervisor, if you wanted and if they were willing, could keep a record of interesting questions or observations. This information could be pretty useful after the viva. But it’s all up to you. If the thought of your supervisor coming adds pressure, then just say no.
