General lack of interest or emotion:
* Indifference
* Unconcern
* Disinterest
* Passivity
* Lethargy
* Numbness
* Coldness
* Detachment
More negative connotations:
* Alienation
* Callousness
* Insensitivity
* Stoicism
* Aloofness
* Disengagement
More specific connotations:
* Emotional apathy: Emotional detachment, emotional flatness, alexithymia
* Motivational apathy: Avolitia, amotivation, inertia
* Social apathy: Social withdrawal, isolation
The best synonym will depend on the specific context. Consider what you want to emphasize about the apathy, and choose the word that best reflects that meaning.