General uncaring:
* Indifferently: This implies a lack of interest or concern.
* Callously: This suggests a cruel or heartless lack of concern.
* Heartlessly: Similar to "callously", emphasizing a lack of emotion.
* Unfeelingly: Implies a lack of empathy or compassion.
Specific uncaring:
* Thoughtlessly: This emphasizes a lack of consideration for others.
* Carelessly: This suggests a lack of attention to detail or consequences.
* Negligently: This implies a lack of responsibility or due care.
* Disdainfully: This conveys a feeling of contempt or disgust.
Other options:
* Apathetically: Implies a lack of passion or energy.
* Coldly: This suggests a lack of warmth or affection.
Ultimately, the best adverb to use will depend on the specific context of your writing. Consider the specific emotions you want to convey and choose the word that most accurately reflects your meaning.