I would not describe his behavior as any of the characteristics we would normally expect at a moment like this in life. Most people would mourn, wonder, get angry, cry, pray, or grieve.
Meursault does none of these. Instead, he is listless, careless, indifferent, and apathetic. He falls asleep and struggles with his exhaustion. It is as if he is a child sitting in a church who is bored and yawning at the pastor's words. Meursault does notice his mother's special friend Perez. This seems to intrigue Meursault, but he doesn't really act on his momentary interest. This apathetic approach to death of someone who should be close makes reading audiences wonder about him at this point. Is he all there? Does he have capacity to feel? Did he have a problem with his mom? This uncaring behavior is not normal for humanity.