When the word that is used in a sentence to introduce some relative clause it is always an essential element which follows. Therefore, no comma is required. Example:
I'm sure that you are lying.
When I leave out the word that, it is still a correct sentence, right? Do I have to use a comma then? Because, when you read the sentence aloud, it kind of feels like there is a pause. Examples
I'm sure you are lying.
I have the evidence right here in my pocket (that) you are lying.
Especially in the second case, I would prefer a comma at the place of the that. Is there a strict rule?