An Actor's Professional Obligation

As an actor your professional obligation is to play your part in such a way that the story is told. The audience is not paying to see you act, they are paying to be told a story. There is no obligation for you to feel anything.

It is okay to play at an emotion instead of feel it. Does it make the experience richer if you are actually feeling what the character is feeling? Yes. But there is no obligation.

Just tell the story folks.

When you remove the pressure of needing to feel, it actually makes it easier for that process to occur.