<p>Empathy is linked to several positive outcomes including health, morality, positive interpersonal relationships, group cooperation and social harmony. It is a complex socioemotional experience that entails cognitive, affective, motivational, and behavioral dynamic, interactive processes. The positive potential of AI agents as human companions is laudable to pursue but there are serious risks and challenges. Despite these risks and challenges, engineers have committed themselves to develop empathy capacity in AI agents. Scholars have noted that AI agents can simulate some aspects of empathy (cognitive empathy) but are known to be limited in their capacity to simulate authentic empathy (known as the empathy gap). The present essay extends this discussion in several directions and highlights multiple gaps in AI empathy. First, we draw attention to the biological, psychological, interpersonal, and developmental processes that pose challenges in the ability for AI to feel authentic empathy for a human. Second, we assert the need for any effort to simulate authentic AI empathy for a human, to account for culture-group processes and differences. And third, we present a heuristic model of empathy to highlight the complexities of simulating authentic AI empathy for humans. We conclude with several important implications on the dangers and limits of AI human empathy, especially as generative AI interactions with children proliferate.</p>