Characters ALWAYS Care - Even If They "Don't Care"

An actor playing the role of someone who "doesn't care" has a lot of work to do.  A playwright will not always hand over the thought process of characters behind their look of disinterest.  If a character doesn't care - there's a reason for it, and it is your job as an actor to find out why.
The important thing to remember is - you HAVE to care.

If you are playing a character who appears not to care in the script or the stage directions state that "he is indifferent to what she says to him" you HAVE to dig deeper! Why does a character appear uninterested? Why is he sitting perfectly still and staring blankly out to the audience? Why does your character state in the script "I don't care."?  Characters, like people, ALWAYS care. They may be hiding their feelings, they may be embarrassed by how the feel, they may feel forced to hide their emotions so as not to be faced with the consequences or they may be yelling "I don't care!" to get someone out of their face because they feel threatened.  If you play this type of role without some kind of feeling or thought process behind your disinterest, the audience will also lose interest in your character and your performance will fall flat!

Some playwrights DO inform the actors of the thought process and explanations of just how the gears are turning inside a character's mind and THIS - is a gift.  If we take the role of Brick, for example in A Cat On A Hot Tin Roof by Tennessee Williams, at the beginning of the play.  His wife Maggie is reaming him out about the fact that they are yet to bear children and she pushes him (or tries to push him) into feeling and expressing some kind of emotion.  During her rants, the script states that Brick speaks "...with a tone of politely feigned interest, masking indifference, or worse, is characteristic of his speech with Margaret." and "...he is not looking at her but into fading gold space with a troubled expression."  and goes on to use words such as "wryly", "indifferently" and "absently".  I adore Tennessee Williams for phrases such as these.  On the surface, one might watch Brick putting up with Maggie's badgering and assume that he must be bored with her or that he feels nothing for her.  This is NOT however the case. Brick has been through the trauma of losing his best friend and has zero interest in taking his wife to bed.  Williams leaves so much room for the actors portraying these roles however, it is important for anyone playing the role of Brick to have a thought process going on in his mind onstage, he MUST feel something towards Maggie (positive or negative) and he must CARE.

Don't deprive a character you are portraying onstage the opportunity to LIVE in front of an audience
because you think it's best to play them as someone who doesn't care.