Carter studies the history of Christian and Islamic healing in the Middle East. He holds a BA in History and Arabic from Baylor University and an MA in Middle Eastern Studies from the University of Texas at Austin. In 2022, he joined the doctoral program in the History of Medicine.

His dissertation project, currently in progress, challenges prevailing narratives of medical modernization and colonization by situating the proliferation of modern mission hospitals in the eastern Mediterranean within longstanding traditions of religious healing, institutional charity, and imperial patronage. The project explores how medical practitioners and patients navigated the ethical frameworks of medical practice in relation to religious commitments, and how Euro-American medical missions reshaped healthcare systems—particularly in Israel/Palestine.

His research has been generously supported by the U.S.-Israel Educational Foundation (Fulbright Israel), the W. F. Albright Institute of Archaeological Research, and the American Historical Association.